quasi three-dimensional, n-bit optical memory based on the ellipsometric principle: model...

Quasi three-dimensional,n-bit optical memory based on theellipsometric principle: model calculations

Roger Jansson, Hans Arwin, and Ingemar Lundstr6m

Model calculations on the ellipsometric memory are presented. The ellipsometric memory is an n-bitoptical memory whose information is extracted by use of the ellipsometric principle. The memory cells ofthe device consist of thin-film multilayer structures, and the information of each memory cell is containedin the optical properties of the thin films. Several thin-film multilayer structures were examined inorder to find out how different choices of layer materials and other system parameters such as layerthicknesses and wavelength affect resolutions and limitations of the ellipsometric memory. Suchcalculations are also useful for optimizing the readout resolution. It was found that it is possible to usememory cells having up to at least eight layers, which would permit 8-bit words to be stored at eachlocation. It was also found that, in principle, several types of materials can be used as layer materials,and various aspects of different choices of materials are discussed.

Key words: Ellipsometric memory, three-dimensional optical memory, ellipsometric multilayercalculations.

Introduction

During the past decade the development of opticalmemories has progressed rapidly. Today there ex-ists disk-based optical storage systems of both non-erasable and erasable type having memory-cell densi-ties of the order of 107 bits/cm 2 and providing a totalstorage capacity of the order of 1 Gbyte of data on thesame medium. The arrival of, for example, morepowerful computer systems or image-analyzing sys-tems will, however, increase the demand for evenhigher storage capacities, which cannot be met byoptical memory systems based on the same principlesas those existing today, owing to their two-dimen-sional nature. In a two-dimensional optical memorythe maximum possible memory-cell density is deter-mined by the diffraction limits of the light used' (andis thus proportional to 1/X2 ). For visible light themaximum memory-cell density is of the order of 108

The authors are with the Laboratory of Applied Physics, Depart-ment of Physics and Measurement Technology, Link6ping Insti-tute of Technology, Link6ping S-581-83, Sweden.

Received 8 September 1993; revised manuscript received 20April 1994.

0003-6935/94/296843-12$06.00/0.c 1994 Optical Society of America.

bits/cm 2. To increase the memory-cell density fur-ther, we need to seek other solutions.

The principle of a three-dimensional optical memorydevice that can eventually provide such a solution haspreviously been presented.2 3 The memory cells ofthis device consist of thin-film multilayer structures,and the information in each memory cell is containedin the optical properties of the thin films. Theoptical readout is based on the ellipsometric prin-ciple,4 i.e., the content of a memory cell is read byanalysis of the state of polarization of a light beamreflected at oblique incidence from the memory cell.The memory will be of the read-only type if the opticalproperties of the layers cannot be changed afterdevice fabrication. A rewritable memory can berealized, for example, with electrochromic or photo-chromic materials.

The principle of the ellipsometric memory is exem-plified in Fig. 1 with a device having four memorycells, in which each cell consists of two thin layers ontop of a substrate. If the optical properties of thetwo layers can be controlled independently, fourdifferent states of polarization of the reflected beamcan be generated, corresponding to the logical states00, 01, 10, and 11 of the memory cell. Each memorycell can thus store a 2-bit word. In a generalizationto n layers it is possible to have 2 different states,

10 October 1994 / Vol. 33, No. 29 / APPLIED OPTICS 6843

Fig. 1. Ellipsometric memory device having four 2-bit memorycells.

which permits an n-bit word to be stored at eachlocation.

With an ellipsometric readout, the state of polariza-tion of the reflected beam is described by the twoellipsometric angles A and T. These angles can bedetermined with a precision better than 0.010.4,5

Furthermore, ellipsometry is in general quite insensi-tive to fluctuations in light intensity, which makes itpossible to accomplish measurements at rather lowlight intensities without losing precision. Hence thelight beam does not need to be focused, but a colli-mated light beam can be used. This opens up thepossibility of parallel processing of several memorycells simultaneously by use of detection techniquesbased on CCD or photodiode arrays.

In a practical device it is also necessary to have anellipsometric readout system with a lateral resolutionbetter than what the fabrication process has. Thetechnical problems connected to this are in principlethe same as those for other surface-based opticalmemories, e.g., magneto-optical memories. For de-termining the lateral resolution limiting the attain-able memory-cell density, several factors must beconsidered. If a collimated light beam is used, thedegree of collimation and the detector size are factorsof importance, while the focusing optics may be alimiting factor if a focused light beam is used. Anoblique incidence also causes the illuminated area tobe increased compared with that of normal incidenceif an unchanged cross section of the incident beam isassumed. Ultimately the lateral resolution limitingthe memory-cell density will be determined by thediffraction limits of the light and the angle of inci-dence chosen. With available techniques, e.g., alaser beam moved by electro-optical methods or bymechanical methods under servo control, it seemsrealistic to have memory cells with an area in therange 1-10 pm 2. The total thickness excluding thesubstrate is n times the thickness of each individuallayer, which may be as thin as a few nanometers.

An important question of a technical nature thatwe have not considered so far is whether or not aworking device with the intended properties can befabricated. In a real device an important require-ment is that thin films with reproducible and stablelayer thicknesses and microstructure can be fabri-

cated. Processing capability is also important, asone must develop methods to deposit a large numberof memory cells side by side on a substrate. In a firstapproach of realizing a device, inorganic films (e.g.,metals, metal oxides, nitrides, and semiconductors)may be easier to implement. Organic films show,however, a much larger variety in properties and areperhaps the best-suited candidates for implementingerasable optical memories.6 The optical and mechani-cal properties of organic materials in addition can betuned by design of their molecular structure, whichgives a large flexibility. Furthermore, organic mate-rials are also often less subject to degradation causedby air and moisture than, for example, metallic mediaand can be deposited by electropolymerization or byspin-coating techniques, leading to lower fabricationcosts as compared with the vapor coating required forthin metal films.

An interesting development is to use thin films ofmaterials with optical properties that can be changedafter device fabrication. Possible materials are con-ducting polymers such as polypyrroles as well asother organic materials. Of special interest are pho-tochromic materials such as spiropyran and dithienyl-ethylene.7 With the latter class of materials it wouldbe possible to prepare large areas with multilayeredstructures in which writing could be done directlywith a focused laser beam. Each layer must thenconsist of different photochromic materials and thewriting must be done with different wavelengths inthe different layers. Ultimately one would like todesign and fabricate multilayer structures with mono-molecular films of organic materials, which haveoptical properties that can be changed individually bysome physical or chemical mechanism.

There are several potential applications of theellipsometric memory. As read-only memories seemmost realistic to realize with existing materials, itcould for example, serve as a complement to existingread-only optical memories such as compact-diskread-only memory for those applications requiring ahigher storage density and/or higher readout speed.Another area in which the ellipsometric memorycould be a powerful alternative is small-capacityapplications such as optical memory cards. A rela-tively small active area could then be used, and aparallel readout would provide a fast readout andmake it possible to construct an optical readoutsystem without any moving parts (except for align-ment), which would extend the lifetime and simplifythe construction of the optical readout system consid-erably.

In this paper we discuss various aspects of theellipsometric memory in more detail and presentcalculations on some thin-film multilayer structuresin order to find out how different choices of layermaterials and other system parameters such as layerthicknesses and wavelength affects resolutions andlimitations of the ellipsometric memory. Such stud-ies are also useful for optimizing the resolution. Allcalculations are made under the assumption of colli-

6844 APPLIED OPTICS / Vol. 33, No. 29 / 10 October 1994

where E = (Eip, Ej) and Er = (Erp, Ers) are thecomplex amplitudes of the electric-field vectors of theincident and reflected waves, respectively. A reflec-tion ellipsometer measures the change in the state ofpolarization caused by the overall reflection andprovides the complex reflectance ratio, defined by4

P = RP = tan IV exp(iA), (2)

Fig. 2. Reflection and transmission of a plane wave by a multi-layer structure sandwiched between semi-infinite ambient andsubstrat e media.

mated light but are also approximately valid forfocused light having small (a few degrees) acceptanceangles. The possibility of utilizing the abundance ofvariations of organic layers, e.g., conducting poly-mers, in ellipsometric memories is also discussed.

Reflection by a Thin-Film Multilayer Structure

Consider the oblique reflection of a polarized opticalplane wave by a stratified structure consisting of Lparallel layers that are sandwiched between semi-infinite ambient and substrate media, as shown inFig. 2. All layers, the ambient and the substrate, areassumed to be linear, homogeneous, and opticallyisotropic so that each medium can be optically de-scribed by its complex refractive index N = n - ik,where n is the index of refraction and k is theextinction coefficient. For a given amplitude andpolarization of the incident wave we can determinethe amplitude and the polarization of the reflectedwave by solving the Maxwell's equations inside eachmedium and by applying appropriate boundary condi-tions at the interfaces. It can be shown that it isadequate to consider two separate situations to deter-mine the amplitude and the polarization of the re-flected wave in terms of those of the incidence wave:one in which the incident wave is linearly polarizedparallel (p) to the plane of incidence and the other inwhich the incident wave is polarized perpendicular (s)to the plane of incidence. The general case of ellipticpolarization can then be obtained by an appropriatelinear combination of these polarizations.

The overall reflection coefficients for p- ands-polarized light are defined by

Rp =E-p (la)

ErSR= Er, (lb)

where the latter equality defines the ellipsometricangles tI and A. These angles are limited between 00and 900 and between 0 and 3600, respectively, andcan be determined with a precision of 0.010 or better.

If the wavelength of the light (), the angle ofincidence (), the thicknesses of the layers (dj), andthe complex refractive indices of the layers (Nj),ambient (NA) and substrate (No), are known, theoverall reflection coefficients can be obtained by calcu-lation of the reflection coefficients for each layersuccessively, starting with the innermost layer:

[rho j~~ = °

Rxj = rx + R-j exp(-i2p;) i= 1 L t1 + rxRx-l exp(-i2p)

whereafter

(3)

RX = RXL, x = p or s. (4)

In Eq. (3), r, x = p or s, are the Fresnel reflectioncoefficients for p- and s-polarized light, which aregiven by

N cos j+j - Nj+i cos I - Ni co N o- j = ,... ,L,Nj cos ->+ + Nj+j cos j

SN+ cos +l Ncosy _ L,SJNj+j COS (Xy+ + Nj os A>j

(5a)

(5b)

respectively. NL+1 - NA and L+1 -4 are the indexof refraction of the ambient and the angle of inci-dence, respectively, and A> are the film phase thick-nesses:

(6)

The complex angles of refraction By can be obtainedfrom Snell's law:

Nosin 0=Nsin4j = ... =NLsin L =NAsin .(7)

As pointed out by Heavens,8 there are severalconditions that must be met when the above theory isapplied. The most important of these for the pres-ent purpose is that the lateral dimensions of the filmsmust be many times their thicknesses. It is there-fore of importance to have thin layers for keepingsmall lateral dimensions. Furthermore, the source


NA

V,_____________------------- ------------------------------------____________._

p = 2,rr dj cos (�j, j = 1, . . . L.k

bandwidth, the beam diameter, and the degree ofcollimation must all be such that the multiple-reflected waves combine coherently.

Model Calculations

In order to test the ellipsometric memory concept, wemade calculations on several material combinationsthat were chosen an illustrative examples of theprinciple, rather than being the best combination ofmaterials for actually building a working device.The choice has not, however, been made completelyarbitrarily, since thin-film multilayer structures con-sisting of the chosen materials have or can eventuallybe realized by use of existing technology. It is alsoour intention to examine if some of the materialcombinations can be used for practical realization of aprototype memory device, as reported elsewhere.39

As a first approach, only nonerasable memory cellsare considered. The layers of a memory cell maythen consist of one or the other of two materials withfixed but different optical properties (correspondingto the logical state 0 and 1). Furthermore, the layersmay have either equal or different thicknesses.

A FORTRAN program has been developed for calcula-tion of ellipsometric parameters for all possible combi-nations of polarization states obtainable for a givenset of optical constants of a multilayer memory cell(there are 2L possible polarization states for a memorycell havingL layers). The possible polarization statesare here represented as points in the A'T plane, butother representations are also possible. It may, forexample, be more advantageous to use some instru-mental parameters that are directly related to theseangles instead (such as the amplitude and the phaseof a detector current). The program also finds thedistance between the two most near-lying polariza-tion states in the AT plane. This distance can beused as a measure of the separation of differentpolarization states and is defined by

Xmin = Min[(Ai - Aj)2+ (Ti - j)2]12>

i, j 2 1...,2. (8)

To be able to discriminate between different polariza-tion states, we need to make Xmin much larger thankXexp, where 8Xexp is defined in terms of the experimen-tal errors B\exp and 8'exp as

8Xexp = [(8Aexp)2 + (8Texp) 2 ]/* 2. (9)

The exact size of the experimental errors depends onthe instrument used, but errors in the measuredvalues of A and T that are less than 0.010 (Refs. 4 and5) are usually attainable.

To illustrate the principle of the ellipsometricmemory, we made calculations on memory cells hav-ing up to eight layers of different combinations of gold(Au) and molybdenum (Mo) on top of a silicon sub-strate. Fabrication of multilayer structures of goldand molybdenum by various sputtering techniqueshave been reported in the literature.'0 -'2 The Au-Mo

Table 1. Complex Refractive Indices at A = 6328 A for the Layer and/orSubstrate Materials Used in the Calculations

Material (Reference) N

Gold 3 0.197 - i3.09Molybdenum' 4 3.70 - i3.54Palladium 5 1.78 - i4.25Polypyrrole' 5 1.49 - iO.385Poly(N-methylpyrrole)' 7 1.58 - iO.0476Amorphous silicon' 8 4.21 - iO.422Amorphous germanium'9 4.70 - il.53Silicon20 3.88 - i.0196Titanium2l 2.15 - i2.92Aluminum 2 2 1.38 - i7.61Platinum 2 3 2.33 - i4.15

combination has also been reported to be fairly stableeven at elevated temperatures because of the lack ofcompound formation and the low solubility of Mo inAu.10 We also made calculations on some othercombinations having layers of other metals or othertypes of materials such as semiconductors or organicmaterials. The complex refractive indices for thematerials discussed in this paper are taken from theliterature'3 -2 3 and are listed in Table 1. Note that,for most materials, we used the bulk values ratherthan the thin-film values of the complex refractiveindices, since literature values of the latter are ingeneral not available except for some special cases.

In Figs. 3(a) and (b) the possible combinations of Aand T for memory cells having different combina-tions of gold and molybdenum on top of a siliconsubstrate are shown in the case of four and eightlayers, respectively. The wavelength and the angleof incidence were chosen to be 6328 A and 700,respectively. For simplicity, the thicknesses of thedifferent layers are assumed to be equal in the twocases and chosen to be 50 A and 70 A, respective-ly. The different polarization states are representedby their corresponding binary code [see Fig. 3(a)], theinnermost layer being assumed to represent the mostsignificant bit and the logical states 0 and 1 denotinggold and molybdenum, respectively. For example,the states 0001 or 00000001 will correspond tomemory cells having a top layer that consists ofmolybdenum, while the other layers consist of gold.The distance Xmin between the two most near-lyingpolarization states is also marked in Fig. 3(a). Thesestates are 0110 and 1001 for the four-layer systemand 10111111 and 00111111 for the eight-layer sys-tem, with Xmin = 1.70 and Xmin = 0.26°, respectively.

A general observation that can be made form thesefigures (observe the scale difference between A and T)and from other similar calculations made on equallythick absorbing layers (k > 0) is that the differentlogical combinations are distributed in groups withinwhich the polarization states tend to lie more close.The most near-lying states can also usually be foundwithin such a group, although exceptions can befound when two groups are located closely to eachother. When the layers are thin (- 50 A for the Au-Mosystem), these groups of states correspond to memory


I I but since this choice in some respects is limited by thew1000 demand of being able to fabricate a thin-film multi-

1100' layer structure having small lateral dimensions, the0100* freedom to choose materials with suitable optical

1110 properties is reduced. For a given material combina-tion, however, there are several parameters that can

0010' 01i M I _ be optimized. The wavelength, for example, cannotXmin 1101 be chosen completely arbitrarily. If only storage

1001 1011- capacity (which is essentially diffraction limited) is0101 0111 considered, the wavelength should be chosen as short

as possible.- The phase thickness terms [Eq. (6)] also0011 indicate that shorter wavelengths permit memory

, , , 150 cells with thinner layers. The difference in optical10 120 130 140 150 properties between the chosen materials may, how-

Delta (degrees) ever, be more advantageous at longer wavelengths.(a) Available light sources must also be considered.

Other factors of importance are the thicknesses of the.. , , , layers and the angle of incidence. In the following

sections we examine in more detail how the separa-tion of the two most near-lying states is affected by

.... :~ ~changes in these parameters for the gold-molybde-num system discussed above.

It should be pointed out, however, that there are. . . also parameters other than just the size of Xmin that

must be considered when parameters are selected.-. : : .A certain combination of materials, wavelength, angle

of incidence, and layer thicknesses may, for example,* . *. : : *result in one or more of the different polarization

states corresponding to situations in which the p or s, , , 140 reflectances are small, which causes the discrimina-

00 110 120 130 140 tion between different polarization states to be moreDelta (degrees) uncertain (at least if there are several such states)

(b) because of increased experimental uncertainty in theossible combinations of A and qI for memory cells having measured ellipsometric angles. Another factor ofombinations of gold and molybdenum on top of a silicon importance is how sensitive Xmin is to small deviationsin the case of (a) four and (b) eight equally thick in layer thicknesses or angle of incidence, since a

'he layer thicknesses are 50 A and 70 A, respectively. certain amount of uncertainty in these quantitiesid X = 6328 A in both cases. must be allowed for.

cells having an equal number of layers of the samematerial; i.e., for a four-layer system there will be fivegroups consisting of permutations of the states 0000,0001, 0011, 0111, and 1111, respectively. When thethickness of the layers increases, a gradual change ofthese groups will take place, and groups correspond-ing to memory cells having the same layer sequenceoutermost will be formed. In the extreme case ofthick layers, only two groups will remain, since thepolarization states of all memory cells having thesame outermost layer will be located closely to eachother because of the opaqueness of this layer.

Optimization

To be able to discriminate between different polariza-tion states, we should make the separation betweenthese states as large as possible. This is of specialimportance for memory cells having many layers, inwhich the polarization states tend to be closer.There are several factors of importance for increasingthe separation of the polarization states. The mostobvious one is perhaps the choice of layer materials,

Layer Thicknesses

To investigate how Xmin depends on the individuallayer thicknesses, we made a more detailed investiga-tion of memory cells having two layers only. Asimilar analysis may in principle be made also formemory cells having more layers, but it will be morecomplicated because of the increased number ofindependent parameters. Figure 4(a) shows the de-pendence of Xmin on layer thickness for a memory cellhaving two equally thick layers of either gold ormolybdenum on top of a silicon substrate. We ob-serve that Xmin has a distinct maximum at a layerthickness of 94 A and that Xmin becomes small atlarger layer thicknesses. The latter is because therelatively high extinction coefficients of the layermaterials in this case cause the uppermost layer tobecome more and more opaque as the thickness of thelayer is increased. Similar calculations were alsomade for memory cells having more layers and forother layer materials (see below). The minimum pand s reflectances of all possible states are also shownin Fig. 4(a). These show that, in this case, there are


32.5

30.0

TO27.5

25.0

22.5

42.5

40.0

37.5

35.0

Oe32.5

30.0

27.5

25.0

22.5

Fig.3. P.different csubstratelayers. T- = 70° ar

12

10

e

.s

x

8

6

0

0 200

15.0

10.0

X5.0

0.0

20.0

15.0

:a 10.0

5.0

0.0

Fig. 4. (a) Xmin

two equally thiclsubstrate. Theall possible polarlayer thickness the outermost la(di) is held consioutermost layerlayer. I and IIandX = 6328 A.

I I 100 no thickness regions in which the reflectances vanishfor any state, since they increase monotonically with

------- 80 layer thickness from those of pure silicon toward aconstant value corresponding to that of the layer

S material having the smallest reflectance (which in60 this case is molybdenum).

In Fig. 4(b) the effect of different thicknesses of the40 two layers is shown. We calculated Xmin as a function

8 of the thickness of the outermost layer when thethickness of the innermost layer is held constant.

20 The angle of incidence and the wavelength are 70°and 6328 A, respectively. It is interesting to note

, 0 that, for each value of the thickness of the innermost400 600 800 1000 layer, there are two peaks in Xmin having approxi-

Layer thickness (A) mately the same magnitude; i.e., there are two differ-(a) ent thicknesses of the outermost layer for which the

separation is optimal. An increase in magnitude ofthe peaks can also be observed for increasing thick-ness of the innermost layer. A comparison with the

d1=200A case of equal layer thicknessses [Fig. 4(a)] also showsthat the magnitudes of the peaks are actually greater

A / \ / \ in Fig. 4(b) for thicknesses of the innermost layer ofmore than 100 A. A more detailed study of thepeak magnitudes and the position of the peaks isshown in Fig. 4(c), in which the optimal values of Xmin,

max(Xmin), and the corresponding values of the outer-most layer thickness (d2opt) are plotted against thethickness of the innermost layer (dj). We observethat, for thicknesses of the innermost layer betweenapproximately 100 A and 250 A, the magnitudes of

________________________ _ , ,the two peaks are almost equal, while there is a50 100 150 200 250 difference in magnitude for other thicknesses of the

innermost layer. For thinner innermost layers theOutermost layer ickness (A) magnitude of the peak corresponding to the thickest

(b) outermost layer is the largest, while the situation isthe opposite if the innermost layer is thicker than 250

250 A. In the latter case the optimal thicknesses of the, , , outermost layer also approaches a constant value (94

o A and 145 A, respectively).200 13

aL Number of Layers

Max(X ~ l10 i For memory cells having more than two layers we. ........ ............... .... -calculated Xmin only in the case in which all layers are

100 -, equally thick. For different thicknesses the analysisA.I 100 g. become more complex, and it is likely that some other

...... ...... . ............. thickness combination will give rise to larger separa-50 tion between the polarization states. In the develop-

. m >ement of a real device, such an analysis will, however,be a way of further optimization.

100 200 300 400 5 0 Figure 5(a) shows the dependence of Xmin on layer100 200 300 400 500 thickness for memory cells having four, five, six,

Innermost layer thickness (A) seven, and eight layers of different combinations of(c) gold and molybdenum on top of a silicon substrate.

versus layer thickness for a memory cell having The angle of incidence and the wavelength are 70°k layers of either gold or molybdenum on a silicon and 6328 A, respectively. Clearly the optimal separa-variation of the minimum p and s reflectances of tion of the different polarization states decreases withrization states, Rpmin and Rsmin, respectively, with increasing number of layers, but even for the caseare also shown. (b) Xmin versus the thickness of with eight layers it is still possible to distinguishyer (d2) when the thickness of the innermost layer between the different logical states by ellipsometry,tant. (c) The variation of max(Xmin) and optimalthickness with the thickness of the innermost as max(Xmin) is 15 times larger than Xexp. The

lenote the two peaks in (b). In all cases, 4 = 700 useful thickness region is, however, decreasing withan increased number of layers, which puts a higher


2.5

2.0

1.5

1.0

0.5

0.0

12.0

10.0

8.0

6.0

4.0

2.0

n

0

2.0

Os

.0

fib

1.5

1.0

0.5

0.050 100 150 200

Layer thickness (A)(a)

... .... .......

.,.

: .~.

2 3 4 5 6 7 8

2.5100

0TO

I0

I

2.0

4

.0

a-50

10

Number of layers

(b)

Fig. 5. (a) Xmin versus layer thickness for four, five, six, seven, andeight equally thick layers of gold or molybdenum on a siliconsubstrate. (b) The variation of max(Xmin) and optimal layer thick-ness with the number of layers. The dashed curves in (b) havebeen added for clarity only. + = 700 and X = 6328 A.

demand on thickness control during fabrication ofmemory cells having many layers. A more detailedinvestigation of how the magnitude of max(Xmin) andoptimal layer thickness vary with the number oflayers [Fig. 5(b)] shows that max(Xmin) decreasesroughly exponentially with the number of layers andthat the optimal layer thickness approaches a con-stant value of 60 A. Similar behavior was alsoobserved for some other high-loss materials, whilepreliminary studies indicate that a different behaviorcan be expected for more weakly absorbing materials.It can also be concluded, by extrapolation of theresults in Fig. 5(b), that a max(Xmin) of the order of theexperimental resolution, i.e., max(xmin) 2Xexp, wouldpermit memory cells with 12-bit words.

Wavelength

As discussed above, the wavelength comes into play inessentially two different ways: partly by direct useof the phase thickness terms [Eq. (6)] and partly bymeans of the wavelength dependence of the opticalproperties of the constituting materials. If we for a

1.5

1.0

0.5

0

0.0 L.

2500

50 100 150 200

Layer thickness (A)

(a).1 1 1 , 1 . I .I .I .150

c(Xmin) N=const

*..* 100.opt

g _<44 dopt fir N=const :a50

I . I . I . I . l . . 0

3500 4500 5500 6500 7500 8500 9500

Wavelength (A)

(b)

Fig. 6. (a) Xmin versus thickness for wavelengths between 2500 Aand 9500 A at r = 70° in the case of four equally thick layers ofdifferent combinations of gold and molybdenum on top of a siliconsubstrate. (b) The variation with wavelength of max(Xmin) andoptimal thickness for the cases of wavelength-dependent andconstant optical properties of the materials. In the latter case thecomplex indices of refraction at X = 6328 A were used for allmaterials.

moment assume that the refractive indices of theconstituting materials do not vary over the wave-length region of interest, a closer examination of Eqs.(2)-(7) shows that the magnitude of Xmin would notchange as long as dj cos j/X remains the same. Fora given angle of incidence a change of wavelength willthus merely result in a shift in the optimal thick-nesses, which is proportional to the wavelength,while the maximum separation between the mostnear-lying polarization states remains the same.If the wavelength dependence of the optical constantsis also accounted for, a different behavior could beexpected since the optical constants usually varyconsiderably with wavelength in the optical part ofthe spectrum. The latter case is illustrated in Fig.6(a), in which Xmin as a function of layer thickness iscalculated for different wavelengths in the case offour equally thick layers of different combinations ofgold and molybdenum on top of a silicon substrate.The angle of incidence was in all cases chosen to be


Osc0

X

X

2.5

v.v

700. A closer examination shows, however, that thelinear relation between optimal thickness and wave-length holds fairly well (but not exactly), as can beseen from Fig. 6(b), in which the variation withwavelength of the magnitude of max(xmin) and opti-mal thickness are shown for the cases of (1) wave-length-dependent and (2) constant optical propertiesof the materials. In the latter case the complexindices of refraction at X = 6328 A were used for allmaterials. Figure 6(b) also shows that X = 6328 A israther close to an optimal choice of wavelength for agold-molybdenum four-layer system when all thelayers are equally thick. Similar results were alsoobtained for other numbers of layers with this mate-rial combination.

2.5

2.0

Os

1-

1.5

1.0

0.5

0.050 100 150 200

Layer thickness (A)

3.0

Angle of Incidence

Another important parameter that must be consid-ered is the angle of incidence. By varying the angleof incidence, one can often increase the sensitivity inthe ellipsometric angles with respect to some specificproperty of a material structure. Since ellipsometrydetermines the ratio of Rp to R5, increased sensitivitymay be expected whenever Rp or R, changes rapidly.If either Rp or R, in addition is small, correspondingto T being close to 0° or 90°, a large increase in thesensitivity may be obtained. Different properties ofthe structure can also be enhanced in the differentcases. It has, for example, been shown23 that thesensitivity for detection of the presence of an inter-face layer between a substrate and a transparentlayer can be optimized near s-wave antireflection,while p-wave antireflection maximizes the sensitivityfor the presence of an overlayer on top of the transpar-ent layer. Since Rp and R, are functions of A, it isclear that this parameter can be used to alter thesensitivity conditions. However, care must be takenin the choice of the angle of incidence to realize a largevalue of the sensitivity without incurring large errorsbecause of uncertainty in the angle of incidence. Fortransparent, nonlayered media, the changes in A withangle of incidence at the Brewster angle (Rp = 0) can,for example, be rather abrupt. For low-loss materi-als, or high-loss materials such as metals, the preflectance does not reach zero as the angle of inci-dence is varied but rather exhibits a minimum (at thepseudo-Brewster angle) whose value depends on thecomplex index of refraction of the material. Thes-reflectance does not in either case have a minimumbut increases monotonically with angle of incidence.For layered media the situation becomes more com-plex, especially for low-loss layers or thin high-losslayers in which it is possible to achieve antireflectionfor both the p and the s waves for several differentcombinations of system parameters. For thickerhigh-loss layers the layered structure itself is of lessimportance, and the result will be more similar tothat of a single material.

To investigate how the gold-molybdenum systemis affected by the choice of angle of incidence, we

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Fig. 7. (a) Variation of Xmin with layer thickness for angles ofincidences between 60° and 800 at X = 6328 A in the case of fourequally thick layers of different combinations of gold and molybde-num on a silicon substrate. (b) The variation of max(xmn) andoptimal layer thickness with the angle of incidence.

calculated Xmin as a function of layer thickness forangles of incidences between 2.50 and 87.50 in the caseof four equally thick layers. Figure 7(a) shows theresults for angles of incidences between 600 and 80.The wavelength is in all cases 6328 A. Curves withappearance similar to those having k = 600 (but withlower magnitude) were also obtained for smallerangles of incidences. A more detailed investigationshows that the thicknesses corresponding to the twopeaks at k = 600 remains essentially the same (57 Aand 84 A, respectively) for angles of incidences lessthan 60° and that the peak corresponding to thelarger layer thickness becomes the largest at less than

400, the latter being manifested as an abruptchange in dopt in Fig. 7(b). For angles of incidencesmore than 60, there is a more gradual change inoptimal layer thickness, which causes the curves tohave a different appearance. This can also be seen inFig. 7(b), which shows how the magnitude of max(xmin)and optimal layer thickness vary with the angle ofincidence. Another study also shows that the loca-tion of the maximum (in this case at 76.3°) is indepen-dent of substrate choice and hence must be caused bythe constituting layer materials. We also found that,


for metallic layers, the maximum is often located inthe vicinity of (within some degrees either below orabove) the pseudo-Brewster angle of the layer mate-rial having the deepest minimum in thep reflectance,91p, and that the maximum tends to approach thisangle with an increasing number of layers. In thiscase, molybdenum has the deepest minimum in Np(15%) at an angle of incidence of 78.60, while gold hasa more shallow minimum in Np (87%) at an angle ofincidence of 70.6°.

Substrate

To investigate the influence of the substrate, we madecalculations for memory cells having four equallythick layers of combinations of gold and molybdenumon top of some substrates other than silicon. Thesubstrate material was either chosen to be one of thelayer materials or to be a different material (titaniumor aluminum). We found that there are differencesboth in magnitude and in position of the peak in Xminfor these materials compared with that of silicon,which shows that the substrate choice can have aconsiderable influence on the results despite the factthat the layers are relatively lossy. For molybde-num, titanium, and gold substrates the differenceswere found mainly in the optimum thickness, but aslight decrease in max(Xmin) was also found for thesesubstrates. For aluminum a significant decrease inmax(xmin) was obtained, while the optimum thicknessremained essentially the same, which indicates that alarge extinction coefficient of the substrate (see Table1) may be unfavorable. It should be pointed out,however, that the differences cannot be explained byan improper choice of angle of incidence for a specificsubstrate material but must be caused by differencesin the complex index of refraction of the substratematerials, since a more detailed study shows that theoptimum angle of incidence is almost the same for allsubstrate materials.

Other Layer Materials

So far we have considered only memory cells withmetallic layers, but in principle any material combina-tion can be used as long as the difference in opticalproperties between the materials is such that it ispossible to discriminate between the different polar-ization states of the reflected beam. We thereforemade calculations on some memory cells havinglayers of materials other than gold and molybdenum,including one with a different metal combination(gold and palladium), one with two semiconductingmaterials (amorphous silicon and amorphous germa-nium), and one with two organic materials (polypyr-role and poly-N-methylpyrrole). The complex indi-ces of refraction of these materials are shown in Table1. The substrate material is silicon in all casesexcept for the case of organic layers, in which it isplatinum. Large-area prototype memory cells hav-ing two or three layers have also been fabricated fromthe two former combinations and are reported else-where,3 9 while the third combination can eventually

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Layer thickness (A)(a)

600

0 25 50 75 100 125 150 175

Layer thickness (A)

(b)

Fig. 8. Variation of Xmin with layer thickness for (a) four and (b)eight equally thick layers of different combinations of gold andpalladium on top of a silicon substrate and of polypyrrole (PPy) andpoly(N-methylpyrrole) (PMPy) on top of a platinum substrate.For comparison, similar calculations are also shown for the gold-molybdenum system (dashed curve). d = 700 and A = 6328 A.

be realized with chemical vapor-deposition tech-niques or by electropolymerization. 2 4 We did not,however, study these in as much detail as the gold-molybdenum system, but we limited ourselves to thecases of four and eight equally thick layers at oneangle of incidence (700) and one wavelength (6328 A).

Figures 8(a) and 8(b) show how Xmin varies withlayer thickness for the four- and the eight-layergold-palladium (Au-Pd) system, respectively. Simi-lar curves for the gold-molybdenum system (dashedcurve) are also included for comparison. Two maindifferences between these systems can be observed:(1) the magnitude of Xmi, is lower for the gold-palladium system than for the gold-molybdenumsystem, and (2) the gold-palladium system shows aless oscillatory behavior in the eight-layer case thandoes the gold-molybdenum system. Since palla-dium has a larger extinction coefficient than molybde-num and since both these materials have largerextinction coefficients than gold, a lower magnitudeof Xmin for the gold-palladium system can be expected


for thicker films since the palladium layers becomemore opaque than the molybdenum layers, and hencethe underlying layers will be more difficult to identifyin the former case. A more detailed study shows,however, that this is only the case for films thickerthan 200 A, while for very thin films (less than 25 A)the main reason for the difference is because of thedifferences in the real part of the complex index ofrefraction. For thicknesses in between, the differ-ences in Xmin are caused by differences in both the realand the imaginary parts of the complex refractiveindex of molybdenum and palladium. The differ-ences in magnitude between the two systems can alsoto some extent be explained by the fact that thechosen angle of incidence (70°) is farther away fromthe optimum chocie for the gold-palladium systemthan for the gold-molybdenum system. The less-pronounced oscillatory behavior of the gold-palla-dium system can probably be explained to a largeextent by the fact that the smaller index of refraction(n) of palladium causes the variation of the phasethickness terms [Eq. (6)] to be less rapid, but themagnitude of the phase thickness terms is also re-duced by the increased extinction coefficient (k) ofpalladium.

Figure 8 also shows similar calculations for one ofthe nonmetallic material combinations, polypyrroleand poly(N-methylpyrrole), which are two conductingpolymers. Some notable differences between thenonmetallic systems and the metallic ones treatedabove are that there are several thickness regions inwhich Xmin become large and that the maxima in Xmin

are obtained for higher thicknesses, which is causedby the lower extinction coefficients of these materials.Max(xmin) is also larger for these systems than for themetallic systems. The eight-layer systems also showsa more rapid variation in Xmin when the layer thick-nesses are increased beyond those corresponding tothe first peaks in Xmin- We also observe that thiseffect is most pronounced for the amorphous silicon-germanium system, both of which are high-indexmaterials. For the polypyrrole-poly(N-methylpyr-role) system the first peak in Xmin also appears athigher layer thicknesses than for the other systems.We found that these differences can be explained inprinciple by the differences in the indices of refractionand the extinction coefficients of the materials asfollows: high-index materials cause Xmin to havelarger values at lower thicknesses than low-indexmaterials. High-index materials also show a more-rapid variation in Xmin as the layer thickness increasesunless this behavior is canceled out by a high extinc-tion coefficient, which causes the phase thicknessterms to become small at higher thicknesses, asdiscussed above.

Discussion

In this paper we study a few material combinationsand do a brief optimization of the ellipsometricmemories in order to find out if it is possible to resolvethe different polarization states with ellipsometry

and to investigate how some of the different systemparameters affect the separation between the polariza-tion states. For construction of a real device a moredetailed investigation has to be made in each specificcase to ascertain which layer and substrate materialsare the most suitable. A careful examination of howthe layer thicknesses should be chosen also needs tobe performed. In the case of eight layers this repre-sents a 10-dimensional problem for a given materialcombination if the wavelength and the angle ofincidence are also included, which indicates that thecomputational effort may be rather large.

In a real device some form of protective layer mayalso be needed. Spacer layers between the activelayers may also be useful for several reasons: thestability of the structure may, for example, be im-proved, and interdiffusion of layer materials may bereduced. Transparent, conducting layers of indium-tin oxide between active layers of electrochromicmaterials may also provide a way to construct electro-optical read-write memories. Calculations show thata 100-A-thick transparent overlayer does not reducemax(Xmin) significantly, while transparent spacer lay-ers of the same thicknesses between the active layersresult in a slightly larger max(Xmin). This also indi-cates that some form of spacer layers can eventuallybe used for optimization purposes.

Another important aspect is the ellipsometric read-out system. The optical components needed fordetermining the polarization state of the output beamdepend on which type of ellipsometer is used. Forthe present application a major demand is a highspeed of measurement without a sacrifice in measure-ment accuracy. One instrument type that can fulfillthese requirements is the phase-modulated ellipsom-eter.25 27 The principle of this instrument is to use apolarizer and a large-amplitude birefringent modula-tor such as a Pockels cell or a piezobirefringent plateto create incident polarized light with a known butrapidly varying polarization state. After reflectionfrom the sample surface, the outgoing light beam ismade linearly polarized by means of an analyzer; bymeasurement of the intensity and the phase variationof the resulting wave it is possible to determine theellipsometric angles A and T. For the present pur-pose of distinguishing between different logical states,some form of decoding logic is also needed. SincePockels cells and piezobirefingent modulators can beoperated in the 100-kHz range,52 8 peak data rates ofthe same order can be obtained. Assuming 8-bitmemory cells, this will permit continuous data ratesof the same order as existing optical disks.29 Byutilizing the possibility of parallel processing, onemay in addition increase the data rate many times.Other types of instruments that eventually couldfulfill the requirements are photopolarimeters, whichhave undergone a rapid development during recentyears. A brief review of the state of the art is givenby Azzam.30 Several different solutions exist for theoptical system, but in general no modulation ormoving parts are included, which makes it possible to


determine the state of polarization at the nanosecondor picosecond time scale with high precision.

Finally, we want to point out that some form ofrelative measurement probably would be required fora real device, since systematic errors usually are moredifficult to eliminate than precision erros. This can,for example, be accomplished by the introduction ofsmall reference cells on the device and the relation ofall measurements to A and for these cells.Relative measurement may also improve the measure-ment speed and reduce the susceptibility to surfacecontamination.

Conclusions

We have shown that it is possible to use ellipsometryto distinguish between the different polarization statesof memory cells having up to eight layers. For agiven material combination it is possible to determinevalues of the wavelength, the angle of incidence, andthe layer thicknesses that give a better separation ofthe different polarization states than others. Thelayer thicknesses that maximize the separation ineach case were also found to be affected by thewavelength choice: a shorter wavelength in prin-ciple causes the optimal layer thicknesses to besmaller, although the decrease in certain wavelengthregions may be canceled by changes in the opticalproperties of the materials. We have also found thatthe choice of layer material as well as substratematerial affects the result significantly. In terms ofXmin the separation between the two most near-lyingpolarization states we found the largest max(Xmin) formore weakly absorbing materials, while the use ofhigh-loss materials as layer materials causes theseparation between the different polarization statesto become small when the layer thicknesses becomelarge. In the case of equally thick layers, we havealso found that high-index materials cause Xmin tohave larger values at lower thicknesses. High-indexmaterials also cause a more rapid variation of Xminwith layer thickness, especially for weakly absorbingmaterials at larger layer thicknesses.

Financial support was obtained from the Engineer-ing Research Council of the National Swedish Boardfor Technical Development.

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quasi three-dimensional, n-bit optical memory based on the ellipsometric principle: model...

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