Method for measuring refractive index and thickness of film and apparatus therefor

A method of measuring at least one of a refractive index, an absorption coefficient and a thickness of a thin film formed on a substrate, said thin film having m (m.gtoreq.1) layers comprising a transparent uppermost layer which is designated a first layer, said method of measuring comprising the steps of;

• selecting a total of (3m+1) parameters which are measures of respective physical properties related to said film and which include a refractive index n(0) of an incident medium through which light passes before impinging on said (m) layers, a refractive index n(j) (j=1 to m) of a j-th layer of said (m) layers, absorption coefficients k(j) (j=2 to m) of a second through m-th layers of said (m) layers, a refractive index n(m+1) of the substrate, an absorption coefficient k(m+1) of the substrate and thicknesses d(j) (j=2 to m) of the second through m-th layers of said (m) layers;
• designating an arbitrary one of the (3m+1) parameters as an unknown parameter X which is a measure of a selected physical property related to said film, the other (3m) parameters being known parameters which are measures of other physical properties related to said film;
• generating monochromatic light having a wavelength .lambda.;
• causing said monochromatic light to impinge on the thin film having said (m) layers at a predetermined incident angle .theta.(0) relative to said first layer after passing through said incident medium, and to be reflected from said layers as S-polarized light and P-polarized light;
• measuring reflectances Rs and Rp of said S-polarized and P-polarized light;
• specifying the unknown parameter X as a function F(X)=a+b+c using measured values of the reflectances Rs and Rp, the wavelength .lambda. and (3m) known parameters;
• a, b and c in this function F(X) being respectively set as follows:
• ##EQU12## Ap, Bp As and Bs in the formulas of a, b and c being respectively set as follows;
• Ap=Rp cos {.phi.(01p)+.phi.(12p)}-cos {.phi.(01p)-.phi.(12p)}
• Bp=Rp sin {.phi.(01p)+.phi.(12p)}-sin {.phi.(01p)-.phi.(12p)}
• As=Rs cos {.phi.(01s)+.phi.(12s)}-cos {.phi.(01s)-.phi.(12s)}
• Bs=Rs sin {.phi.(01s)+.phi.(12s)}=sin {.phi.(01s)-.phi.(12s)}
• .rho.(01p), .rho.(01s), .rho.(12p), .rho.(12s), and .phi.(01p), .phi.(01s), .phi.(12p), .phi.(12s) in the formulas of a, b and c being respectively set as follows;
• r(01p).ident..rho.(01p) exp {i.phi.(01p)},
• r(01s).ident..rho.(01s) exp {i.phi.(01s)},
• r'(12p).ident..rho.(12p) exp {i.phi.(12p)},
• r'(12s).ident..rho.(12s) exp {i.phi.(12s)},
• r(01p) and r(01s) being respectively set to amplitude reflectances of the P-polarized light and the S-polarized light on an interface between the incident medium and the first layer;
• and
• r'(12p) and r'(12s) are respectively set to amplitude reflectances of the P-polarized light and the S-polarized light provided when said monochromatic light is incident to (m-1)-thin film layers except for the first layer in the incident medium having the same refractive index as the refractive index of the first layer;
• determining a value of said selected physical property of the film by determining said unknown parameter X through solving numerically an equation F(X)=0;
• and
• utilizing the value of said selected physical parameter of the film determined in said determining step.

An apparatus for measuring at least one of a refractive index, an absorption coefficient and a thickness of a layer of a thin film formed on a substrate, in which the thin film has m (m.gtoreq.1) layers comprising at least a transparent uppermost layer which is designated a first layer, in which a measured sample having the thin film and the substrate includes a total of (3m+1) parameters comprising a refractive index n(0) of an incident medium, a refractive index n(j) (j=1 to m) of a j-th layer, absorption coefficients k(j) (j=2 to m) of second to m-th layers, a refractive index n(m+1) of the substrate, an absorption coefficient k(m+1) of the substrate, and thickness d(j) (j=2 to m) of the second to m-th layers, and in which (3m) of the (3m+1) parameters are known and one of the (3m+1) parameters is unknown, said apparatus comprising:

• a light source device for selectively emitting monochromatic beams of s-polarized light and p-polarized light, respectively;
• a support, disposed on an optical path of said s-polarized light and said p-polarized light, for supporting said sample such that said s-polarized and p-polarized lights are respectively incident on said thin film at a predetermined incident angle;
• a photo-sensor, disposed on an optical path of said s-polarized and p-polarized lights so as to receive said s-polarized light and said p-polarized light after they are reflected from said thin film, for outputting a first signal corresponding to said reflected s-polarized light and a second signal corresponding to said reflected p-polarized light;
• a calculation device, electronically connected to said photo-sensor, for receiving said first signal and said second signal;
• and
• a numerical condition setting device, electrically connected to said calculation device, for setting the value of each of (3m) known parameters, a value of said incident angle .THETA.(0), and a value of wavelength .lambda. of said monochromatic beam, and for outputting respective signals corresponding to said set values,
• said calculation device comprising:
• a reflectance determining circuit, electrically connected to said photosensor, for determining a reflectance Rs of said s-polarized light and a reflectance Rp of said p-polarized light on the basis of said first and second signals from said photo-sensor, and for outputting a third signal representing said determined reflectance Rs of said s-polarized light and a fourth signal representing said determined reflectance Rp of said p-polarized light:
• and
• an unknown parameter determining circuit, electrically connected to said numerical condition setting device and said reflectance determining circuit and storing a function of F(n(0), n(j), k(j), d(j), .THETA.(0), .lambda., Rs, Rp) which represents a relation among said (3m+1) parameters, said incident angle, the wavelength of said monochromatic beam and reflectances of said s-polarized and p-polarized lights, for substituting values of each of said (3m) known parameters, and values of said incident angle, said wavelength of said monochromatic beam and said reflectances into said function on the basis of said signals from said numerical condition setting device and third and fourth signals from said reflectance determining circuit for numerically solving an equation of F(x)=0 to thereby obtain a value of the unknown parameter X, and for specifying said obtained value as a value of said unknown parameter to thereby output a signal representing said specified value.

An apparatus for measuring at least one of a refractive index, an absorption coefficient and a thickness of a thin film formed on a substrate, said thin film having m (m.gtoreq.1) layers comprising a transparent uppermost layer which is designated a first layer, and

• a total of (3m+1) parameters which are measures of respective physical properties and which include a refractive index n(0) of an incident medium through which light passes before impinging on said (m) layers, a refractive index n(j) (j=1 to m) of a j-th layer of said (m) layers, absorption coefficients k(j) (j=2 to m) of second through m-th layers of said (m) layers, a refractive index n(m+1) of the substrate, an absorption coefficient k(m+1) of the substrate, and thickness d(j) (j=2 to m) of the second through m-th layers of said (m) layers;
• one of the (3m+1) parameters being an unknown parameter X which is a measure of a selected physical property related to said film, the other (3m) parameters being known parameters which are measures of other physical properties related to said film;
• a support for supporting a measured sample;
• a light source device for selectively irradiating a monochromatic beam of each of S-polarized light and P-polarized light to said measured sample at a predetermined incident angle;
• a photo-sensor for receiving a light beam reflected from said measured sample and photoelectrically converting said reflected light beam;
• a computer for determining a value of said selected physical property of the film by determining said unknown parameter X through calculating an equation F(X)=0 based on an output of said photo-sensor,
• this function F(X) being set to F(X)=a+b+c and a, b and c in this function F(X) being respectively set as follows:
• ##EQU14## Ap, Bp As and Bs in the formulas of a, b and c being respectively set as follows;
• Ap=Rp cos {.phi.(01p)+.phi.(12p)56 -cos {.phi.(01p)-.phi.(12p)}
• Bp=Rp sin {.phi.(01p)+.phi.(12p)}-sin {.phi.(01p)-.phi.(12p)}
• As=Rs cos {.phi.(01s)+.phi.(12s)}-cos {.phi.(01s)-.phi.(12s)}
• Bs=Rs sin {.phi.(01s)+.phi.(12s)}-sin {.phi.(01s)-.phi.(12s)}
• .rho.(01p), .rho.(01s), .rho.(12p), .rho.(12s), and .phi.(01p), .phi.(01s), .phi.(12p), .phi.(12s) in the formulas of a, b and c being respectively set as follows;
• r(01p).ident..rho.(01p) exp {i.phi.(01p)},
• r(01s).ident..rho.(01s) exp {i.phi.(01s)},
• r'(12p).ident..rho.(12p) exp {i.phi.(12p)},
• r'(12s).ident..rho.(12s) exp {i.phi.(12s)},
• r(01p) and r(01s) being respectively set to amplitude reflectances of the P-polarized light and the S-polarized light on an interface between the incident medium and the first layer;
• r'(12p) and r'(12s) being respectively set to amplitude reflectances of the P-polarized light and the S-polarized light provided when said monochromatic light is incident to (m-1)-thin film layers except for the first layer in the incident medium having the same refractive index as the refractive index of the first layer;
• and for outputting the value of said selected physical parameter of the film.