CN1715832A - Method for measuring single side polishing substrate epitaxial film thickness and optical parameter - Google Patents

Abstract

The method of measuring the thickness and optical parameters of epitaxial film on single-sided polished substrate is based on the characteristic that the maximum transmissivity of the epitaxial film structure on substrate depends only on the substrate material. The method includes zooming the measured transmissivity extreme values TM and Tm, correcting TM and Tm in considering the effect of the spectral width of the spectrophotometer on the transmissivity to obtain corrected values TM' and Tm', calculating the refractive index n1 of the film in the transparent area and the weak absorption area, and calculating based on the transmissivity extreme value condition the film thickness d1, the average film thickness d, the film refractive index n within the transmissive range and film absorption index alpha. The method is simple and practical.

Description

The measuring method of single side polishing substrate epitaxial film thickness and optical parametric

Technical field

The invention belongs to field of measuring technique, relate to Film Optics and measure specifically a kind of method of measuring single side polishing substrate epitaxial film thickness and optical parametric.Be applied to backing material and be single-sided polishing and when being transparent, utilize transmission spectrum that the thickness and the optical parametric of film are measured with respect to epitaxial material.

Background technology

In the growth of partly leading material, often use growth technology epitaxial growth film on substrate, as metal organic chemical vapor deposition (MOCVD) growing method.Be grown in the many epitaxial loayer films on the substrate, as polycrystalline Si, GaN, AlGaN etc. usually are used to make photoelectric device.Performance for forecasting institute is made photoelectric device better designs device, must at first measure the refractive index of epitaxial film and absorption coefficient with wavelength change.

At present, the measurement of epitaxial film refractive index has several different methods, as the example that is measured as with the GaN film of extension on the Sapphire Substrate, a kind of measuring method commonly used records its refractive index with the prism-coupled method exactly, as Begmann M.J.Ozgur Uand Cassy H.C.et.al.Ordinary and extraordinary refractive indices for AlGaN epitaxiallayers[J] Appl.Phys.Lett.1999 Vol 75:67-69, article is disclosed to be exactly this method.There are following two aspect deficiencies in this prism-coupled method:

(1),, needs use 475.9nm, 476.5nm, 488nm, 496.5nm, the Ar of 514.5nm particularly to the light source requirements harshness to the having relatively high expectations of surveying instrument ⁺The HeNe laser instrument of ion laser, 632.8nm, 676.2nm, the semiconductor laser of 968.3nm, 729.2nm, multiple laser instruments such as the Ti sapphire laser of 837.3nm.These instrument costlinesses, common laboratory does not satisfy the requirements.

(2) measurement function is limited, can only measure refractive index, and the energy measurement absorption coefficient is not with wavelength change.

Another kind of commonly used method is based on the measurement of spectrophotometer transmission spectrum, because transmission spectrum is more cheap, is the common instrument of exosyndrome material, thereby is a kind of simple, less method of cost with transmission spectrum to the measurement that epitaxial thin film material carries out optical parametric.Nineteen eighty-three, Swanepoel has introduced the method for the thickness and the optical parametric of polysilicon being measured with transmission spectrum, referring to Swanepoel, Determination of the thinckness and optical constants of amorphoussilicon J.Phys.E.:Sci.Instrum.16 1214-22.This method is successful in 1997 and 1999, and to be applied to GaN be the measurement of film.Respectively referring to Brunner D.Angerer H.and Bustarret E.et.al.Opticalconstants of epitaxial AlGaN films and their temperature dependence[J] J.Appl.Phys.1997.Vol 82:5090-5096 and Muth J.F.Brown J.D.and Johnson M.A.L.et al.Absorption coefficientand refractive index of GaN, AlN and AlGaN MRS Internet J.Nitride Semicond.Res.4SI, two pieces of documents of G5.21999.Utilize this transmission spectrum not only to record the thickness and the refractive index of material easily, and can record absorption coefficient simultaneously with the wavelength change rule.But these maximum deficiencies of utilizing the measuring method of spectrophotometer transmission spectrum are to measure the backing material of the epitaxial growth film of twin polishing, and the backing material of the epitaxial growth film of energy measurement single-sided polishing not, in the practicality, because many photoelectric devices do not need specially to be produced on the film of twin polishing substrate epitaxial, and the backing material of twin polishing is more expensive with respect to the backing material price of single-sided polishing, thereby not only caused the significant wastage of cost, also limited the range of application of transmission spectrum measuring method.

The content of invention

The objective of the invention is to solve the deficiency of transmission spectrum measuring method, a kind of measuring method of measuring single side polishing substrate epitaxial film thickness and optical parametric is provided, to solve in the practicality problems of measurement single side polishing substrate epitaxial growing film parameter.

Technical scheme of the present invention is achieved in that

The principle of foundation of the present invention is: when the energy gap of epitaxial film than the energy gap of backing material hour, the film growth that can equivalence be an absorption is on a transparent substrate, as Fig. 1.If the thickness of film is d, complex index of refraction is n=n-ik.In the formula, n is a film refractive index, is a real number, and parameter k is the amount relevant with absorption coefficient, is expressed as k=α λ/4 π.When the energy of incident light during less than the energy gap of membraneous material, parameter k compares usually with general refractive index n and is much smaller, and can suppose k=0 like this, and then complex index of refraction n just approximates film refractive index n.The refractive index s of backing material is known, its absorption coefficient _s=0.The refractive index of surrounding air is n _o=1.According to incident light energy difference, membraneous material absorbs different situations to incident light, transmission spectrum can be divided into: clear area, weak uptake zone, four parts in middle uptake zone and strongly absorbing region.Wherein, in absorption coefficient=0 of clear area film, the value of transmission spectrum is bigger; Absorption coefficient is very little in weak uptake zone, and owing to the absorption of film to light, transmission spectrum begins to reduce, but can be considered identical with the clear area when absorption coefficient is very little; Absorption coefficient is bigger in middle uptake zone, the influence that reduces mainly to be subjected to absorption coefficient of transmission spectrum; The transmission spectrum that influences in the strongly absorbing region owing to α reduces strongly.

If film thickness d is uniformly, tangible interference fringe will appear, and the appearance of interference fringe is the result owing to interference effect, as shown in Figure 1.By the ultimate principle of penetrating the spectrum interference effect that provides among Fig. 1 as can be known, incident light is vertically to inject the GaN film in the air, by film GaN and substrate sapphire, finally enter in the air again, generally, backing material is compared with epitaxial thin film material and is wanted much thick, and difference is usually in the level of several magnitudes, so the formation of interference fringe is mainly because directly emergent light and epitaxial film primary event interference of light cause.Can be used for calculated thickness and optical constant according to the situation of interference fringe.

If light vertical incidence then transmission spectrum occur interfering the condition of extreme value to be:

2nd=m λ (wave number m is an integer) (1)

When wave number m is integer, interfere to make striped brightness be strengthened to maximum, when wave number m is half-integer, interfere to make the striped brightness deterioration to minimum.(1) though formula has comprised the information of film refractive index n and thickness d simultaneously, because they are to occur with the form of product, so refractive index n and thickness d can not be determined simultaneously.As seen only utilize (1) formula can not finish measurement to film thickness and optical parametric.

For this reason, consider that first substrate is the situation of twin polishing.The transmission spectrum of film can be expressed as lambda1-wavelength λ in theory, refractive index of substrate s, and film refractive index n, the function of film thickness d and film absorption factor alpha, promptly

T＝T(λ，s，n，α) (2)

Backing material refractive index s is known and be twin polishing, and the imaginary part k of membraneous material refractive index is zero, and energy can be expressed as less than the incident light transmissivity of energy gap like this:

Parameter A, B, C, D, , x are expressed as follows:

A＝16n ²s

B＝(n+1) ³(n ²+s ²)

C＝2(n ²-1)(n ²-s ²) (4)

D＝(n-1) ³(n-s ²)

＝4πnd/λ

x＝exp(-αd)

When reaching extreme value, transmissivity is expressed as follows:

$T_M=\frac{\mathrm{Ax}}{B-\mathrm{Cx}+{\mathrm{Dx}}^2}---\left(5\right)$

$T_m=\frac{\mathrm{Ax}}{B+\mathrm{Cx}+{\mathrm{Dx}}^2}$

To this transmissivity maximum value T _MFurther analyze with Tm, it is a wavelength X as can be known, the continuous function of refractive index n (λ) and parameter x (λ); In addition, on maximum value and minimizing envelope, any minimal value can find a corresponding transmissivity T on the maximum value envelope _M, any maximum value can find a corresponding transmissivity Tm on the minimal value envelope, as the target T of institute among Fig. 2 _MWith the curve of Tm, so just can utilize interpolation method to try to achieve two transmissivity extreme value T of each extreme value wavelength correspondence _MAnd Tm.

In absorption coefficient=0 of clear area membraneous material, the x=0 in the formula (4) just.In first expression formula in each the expression formula substitution formula (5) in (4), can get:

$T_M=\frac{2s}{s^2+1}---\left(6\right)$

By (6) formula as can be known, the maximum value of interference fringe only depends on the refractive index of backing material, and is irrelevant with other factors.Without measurement, the refractive index of substrate known to only relying on just can calculate different wave length institute to deserved refractive index maximum value like this.In second expression formula in each the expression formula substitution formula (5) in (4), can get:

$T_m=\frac{{4n}^{2}s}{n^4+n^2(s^2+1)+s^2}---\left(7\right)$

Solving refractive index is:

n＝[M+(M ²-s ²) ^1/2] ^1/2 (8)

Wherein:

$M=\frac{2s}{T_m}-\frac{s^2+1}{2}---\left(9\right)$

Because transmissivity minimal value T _mBe the function of film refractive index n and refractive index of substrate s, therefore, as long as know T _mJust can calculate refractive index n by above-mentioned several expression formulas.But having solved, top (6)～(9) formula when backing material is twin polishing, how to utilize the clear area to find the solution the problem of film refractive index, but owing to used the value of transmissivity in calculating, and the single-sided polishing substrate has been because the rough property of one side has exactly influenced the value of transmissivity, so will be very big with the value deviation of the refractive index of top method calculating single side polishing substrate epitaxial film directly.Below we solve the computational problem of epitaxial film refractive index on the single-sided polishing substrate.

One. solve the refractive index problem of clear area and weak uptake zone

Because no matter backing material is twin polishing or single-sided polishing, film always is grown in the one side of polishing, the quality of epitaxial film should be identical, thus the selection of substrate in essence for the character of epitaxial thin film material less than influence, it has only influenced the light transmission rate of substrate.Because a single-sided polishing substrate not side surface of growth material is rough, its coarse scattering that causes light, light is lost and can not be arrived detector, this is the reason that causes the transmissivity of single side polishing substrate epitaxial film and twin polishing substrate epitaxial film to differ.And it is to be noted that the coarse incident light influence for different wavelength on surface is different, and wavelength is short more, and its influence is big more.If imagination can be recovered the information of losing owing to substrate is coarse, just can utilize the refractive index of formula (6)-(9) calculating film.

Owing to change under the little situation in light intensity, to same wavelength incident light because the variation of the coarse transmissivity that causes of substrate is a same ratio.Thereby by formula (6) as can be known, the value of transmissivity maximum value only by the refractive index decision of substrate, because the refractive index of substrate is known, just can be counted the maximum value T that draws at certain wavelength transmission spectrum without measuring like this when the substrate twin polishing _MBecause the variation that the transmissivity of coarse incident light to same wavelength causes is a same ratio, in the time of so just can be with single-sided polishing to transmissivity extreme value T _{M is single}And T _{M is single}Amplify in proportion, magnification ratio is T _M/ T _{M is single}, the scaling formula is:

T _M=T _{M is single}* T _M/ T _{M is single}

T _m=T _{M is single}* T _M/ T _{M is single}(10)

By to transmissivity extreme value T _{M is single}And T _{M is single}Amplify the information of losing owing to scattering in the time of just can recovering single-sided polishing in proportion, and then utilize formula (7)～(9) to draw the refractive index of membraneous material.In order to draw the refractive index of membraneous material more accurately, the present invention considers the influence of spectrophotometer spectral width to transmissivity, to the transmissivity extreme value T behind the convergent-divergent _MAnd T _mCarry out following correction:

When utilizing transmission spectrum to calculate the membraneous material refractive index, because the spectrophotometer in the transmission spectrum always has certain spectral width S, the light that shines like this on the film is not real monochromatic light just, but wavelength coverage is the approximate monochromatic light of λ ± S/2, this approximate monochromatic light source can influence to some extent to the film interference striped.In fact, the polyenergetic of incident light makes the maximum value T of interference fringe _MBecome big, and the minimum value T of interference fringe _mDiminish.If between two maximum value or the spacing between two minimal values be w, the change amount Δ T of interference fringe extreme value T is directly proportional with the transmissivity T of striped and the width of spectrometer irradiates light, reduces along with the increase of the spacing w between the extreme value, and following relationship is arranged

ΔT＝(TS/w) ² (11)

Because the transmission spectrum maximum value behind the single side polishing substrate epitaxial film scaling has been theoretic maximum value, should not increase to some extent again, therefore transmission spectrum minimal value T is all tackled in the correction of being done for the single side polishing substrate epitaxial film _mCarry out, so adopt following formula film transmission spectrum extreme value T _MAnd T _mRevise:

T _M′＝T _M

Tm′＝Tm-(Tm×S/w _m) ²-(TM×S/w _M) ² (12)

Here the width w between two extreme values is shown below:

w _M＝λ _m(i-1)-λ _m(i+1)

w _m＝λ _M(i-1)-λ _M(i+1) (13)

Wherein be designated as M down and represent transmission spectrum maximum value, being designated as m represents the transmission spectrum minimal value down.

To revised transmissivity extreme value T _M' and T _m' utilize formula (7)～(9) again, just can obtain the refractive index n of the film of clear area and weak uptake zone ₁

Two. solve the refractive index problem of film thickness and general uptake zone and strongly absorbing region and described refractive index is revised again

At first, calculate the thickness of film,, between adjacent peaks and trough, have following formula to set up promptly according to interfering extremum conditions formula (1):

2n ₁d＝m′λ ₁

(m ' be integer) (14)

2n ₂d＝(m′-1/2)λ ₂

Wherein m ' is for interfering the wave number of maximum value correspondence, λ ₁Be the wavelength of this moment, n ₁For wavelength at λ ₁The time correspondence refractive index; (m '-1/2) is for interfering the wave number of minimal value correspondence, λ ₂Be the wavelength of this moment, n ₂For wavelength at λ ₂The time correspondence refractive index, and λ ₁＜λ ₂Because refractive index n has following character: in the zone of incident light energy much smaller than the membraneous material energy gap, i.e. the long zone of wavelength, the value of refractive index n changes slowly.So can make n at the longer wavelength place ₁=n ₂, have like this

m′λ ₁＝(m′-1/2)λ ₂ (15)

The value that obtains m ' is

$m\text{'}=\frac{{\mathrm{\λ}}_2}{2({\mathrm{\λ}}_2-{\mathrm{\λ}}_1)}---\left(16\right)$

Because the value of m ' is an integer,, the result who tries to achieve do not have error so being rounded the value that obtains afterwards.Again owing to be continually varying and the thickness of film is constant at the transmission spectrum medium wavelength, so the value of wave number also should be continually varying, and the difference between the promptly adjacent extreme value between the wave number is a half-integer 1/2.Obtain so just can releasing the pairing wave number m of all transmissivity extreme values after the value of definite several m '.

Then, wave number m substitution formula (14) is obtained the film thickness d of each extreme point correspondence in clear area and the weak uptake zone ₁, ask film thickness d then ₁Arithmetic mean finally obtain the average thickness d of film thickness.

Because interfere extremum conditions formula (1) to be confined to clear area and weak uptake zone incessantly, but be applicable to whole transmission spectrum district, therefore film thickness and wave number have been known, just can utilize formula (1) to try to achieve the value of each extreme point refractive index n, when trying to achieve each extreme point refractive index n to the refractive index n of film in clear area and weak uptake zone ₁Revise.

Three. solve the problem of film absorption coefficient

For the measurement of absorption coefficient, generally adopt following formula to calculate:

α＝-1/dln(1/B{A+[A ²+2BT(1-R ₂R ₃)] ^1/2} (17)

Parameter A in following formula, B is

A＝-(1-R ₁)(1-R ₂)(1-R ₃)

B＝2T(R ₁R ₂+R ₁R ₃-2R ₁R ₂R ₃) (18)

R ₁, R ₂, R ₃Be air and film, film and substrate, the reflection coefficient between substrate and the air.Be defined as

R ₁＝[(1-n)/(1+n)] ²

R ₂＝[(n-s)/(n+s)] ² (19)

R ₃＝[(s-1)/(1+s)] ²

N is a film refractive index, and s is a refractive index of substrate.T is a transmissivity, and it is neither interfere T when very big _M', neither interfere the T when minimum _m', but use T _M' and T _m' geometrical mean, calculating formula is:

$T=\sqrt{T_M^{\′}\×T_m^{\′}}---\left(20\right)$

Thereby obtain absorption coefficient, so just finished measurement single side polishing substrate epitaxial material thickness and optical parametric.

Describe according to above-mentioned theory, measuring process of the present invention is as follows:

1) long epitaxial film on the single-sided polishing substrate is carried out the measurement of transmission spectrum, obtain transmission spectrum extreme value data T _{M surveys}And T _{M surveys}, and their pairing extreme value wavelength X _MAnd λ _mAccording to measurement result in clear area and weak uptake zone to T _{M surveys}And T _{M surveys}Carry out Lagrange's interpolation and calculate, try to achieve pairing two the transmissivity extreme value T of each extreme value wavelength _{M is single}And T _{M is single}

2) according to formula $T_M=\frac{2s}{s^2+1}$ Calculate the pairing theoretical transmissivity maximum value T of each extreme value wavelength with the refractive index s of backing material _M, then to 1) in the transmissivity extreme value T that obtains _{M is single}And T _{M is single}Carry out scaling, the scaling ratio is T _M/ T _{M is single}, the scaling formula is T _M=T _{M is single}* T _M/ T _{M is single}And T _m=T _{M is single}* T _M/ T _{M is single}, obtain the extreme value transmissivity T behind the scaling _MAnd T _m

3) the present invention considers that the spectrophotometer spectral width is to the influence of transmissivity, to the transmissivity extreme value T behind the convergent-divergent in the transmission spectrum _MAnd T _mUtilize formula T _M'=T _MAnd T _m'=T _m-(T _m* S/w _m) ²-(T _M* S/w _M) ²Revise, wherein the width between two extreme value transmissivities is w _M=λ _{M (l-1)}-λ _{M (l+1)}And w _m=λ _{M (i+1)}-λ _{M (i+1)}, S is spectrophotometric spectral width, obtains revised extreme value transmissivity T _M' and T _M';

4) to revised extreme value transmissivity T _m', utilize formula n ₁=[M+ (M ²-s ²) ^1/2] ^1/2, and formula $M=\frac{2s}{T_m^{\′}}-\frac{s^2+1}{2}$ Calculate the refractive index n of clear area and weak uptake zone ₁

5) two adjacent extreme value wavelength X that record according to transmission spectrum in clear area and weak uptake zone ₁And λ ₂(λ ₁Corresponding maximum value wavelength, λ ₂Corresponding minimal value wavelength and λ ₁＜λ ₂), utilize formula $m^{\′}=\frac{{\mathrm{\λ}}_2}{2({\mathrm{\λ}}_2-{\mathrm{\λ}}_1)}$ Determine the pairing wave number m ' of transmissivity maximum value, this m ' is an integer, differ the wave number m of half-integer 1/2 this characteristic correspondence when knowing all transmissivity extreme values by inference then according to wave number between the adjacent extreme value, the wave number m and the refractive index n that have obtained ₁, utilize transmissivity extremum conditions 2n ₁The film thickness d of correspondence when d=m λ obtains clear area and weak uptake zone and the transmissivity extreme value occurs ₁, ask film thickness d then ₁Arithmetic mean obtain the average thickness d of film;

6) because transmissivity extremum conditions 2nd=m λ sets up all transmission spectrum zones, utilize transmissivity extremum conditions 2nd=m λ and the film average thickness d and the wave number m that obtain like this, obtain the refractive index n of the film in the transmission spectrum scope, simultaneously to n ₁Revise;

7) ask T _M' and T _m' geometrical mean $T=\sqrt{T_M^{\′}\×T_m^{\′},}$ Utilize formula then

α＝-1/dln(1/B{A+[A ²+2BT(1-R ₂R ₃)] ^1/2}

Try to achieve absorption coefficient, in the formula

A＝-(1-R ₁)(1-R ₂)(1-R ₃)

B＝2T(R ₁R ₂+R ₁R ₃-2R ₁R ₂R ₃)

R ₁, R ₂, R ₃Be air and film, film and substrate, the reflection coefficient between substrate and the air is expressed as

R ₁＝[(1-n)/(1+n)] ²，R ₂＝[(n-s)/(n+s)] ²，R ₃＝[(s-1)/(1+s)] ²

Through the later thickness that just can obtain epitaxial film of top step, refractive index and absorption coefficient have been finished whole measurements.

Method of the present invention is simple, lower to equipment requirements, has solved the single side polishing substrate epitaxial film and can not use the problem that transmission spectrum is measured thickness and optical parametric; Reduced the requirement of epitaxial film thickness and optical parameter measurement simultaneously, reduced expense, significant values has been arranged in actual applications backing material.

Description of drawings

Fig. 1 is to be the basic principle schematic of the epitaxial thin film material transmission spectrum of example with GaN

Fig. 2 is to be the transmission spectrum of epitaxial film on the single-sided polishing substrate of example with GaN

Fig. 3 is the index of refraction diagram of GaN film

Fig. 4 is the absorption coefficient figure of GaN film

Embodiment

Below in conjunction with example concrete measuring process of the present invention is described.

With metal organic chemical vapor deposition (MOCVD) method extension GaN membraneous material on Sapphire Substrate, usually Sapphire Substrate is much thicker than the GaN film, the GaN film thickness usually between 0.5-5.0 μ m, and the thickness of Sapphire Substrate be generally 330 μ m be the GaN film tens to hundred times.The refractive index s of Sapphire Substrate is known, as table 1.Sapphire absorption coefficient in the transmission spectrum scope of being surveyed _s=0.

The refractive index of table 1 Sapphire Substrate between 355-1064nm

Wavelength	355	442	458	488	515	532	590	633
									Refractive index	1.79598	1.78038	1.77843	1.7753	1.77304	1.7717	1.76804	1.7659

Wavelength	670	694	755	780	800	820	980	1064
									Refractive index	1.76433	1.76341	1.76141	1.76068	1.76013	1.75961	1.75607	1.75449

This example is measured accurate thickness, optical parametric refractive index and the absorption coefficient of GaN film by following process.

(1) the extension GaN film that is grown on the single-sided polishing Sapphire Substrate is carried out the measurement of transmission spectrum, obtain transmission spectrum extreme value data T _{M surveys}And T _{M surveys}, and their pairing wavelength X, as table 2.

Extension GaN film on the table 2 single-sided polishing Sapphire Substrate carries out the measurement result of transmission spectrum

Wavelength (nm)	700	726	755	786	821	858	900	946
									T M surveys(100％)	0.4572		0.4644		0.4716		0.4775
T M surveys(100％)		0.4117		0.4157		0.4203		0.4221

Table 2 is at first handled clear area and weak uptake zone, has only write out the value of wavelength more than 700nm.

(2) actual measurement transmission spectrum extreme value T _{M surveys}And T _{M surveys}Carry out Lagrange's interpolation and calculate, obtain pairing two the extreme value transmissivity T of each extreme value wavelength _{M is single}And T _{M is single}, as shown in table 3.

Two transmissivity extreme values of each the extreme value wavelength correspondence that obtains after the table 3 pair measurement result interpolation calculation

Wavelength (nm)	700	726	755	786	821	858	900	946
									T M is single(100％)	0.4572	0.4608	0.4644	0.4680	0.4716	0.4746	0.4775	0.4801
T M is single(100％)	0.4089	0.4117	0.4138	0.4157	0.4182	0.4203	0.4215	0.4221

(3) according to formula $T_M=\frac{2s}{s^2+1}$ Theoretical transmissivity maximum value T when calculating the extreme value wavelength with the refractive index s of the backing material that obtains by the data in the table one _M, then to transmissivity extreme value T _{M is single}And T _{M is single}Carry out scaling, the scaling ratio is T _M/ T _{M is single}, obtain the extreme value transmissivity T behind the scaling _MAnd T _m, as shown in table 4.

Extreme value transmissivity T after table 4 conversion _MAnd T _m

Wavelength (nm)	700	726	755	786	821	858	900	946
									Conversion back T M(100％)	0.8582	0.8585	0.8587	0.8589	0.8591	0.8594	0.8596	0.8598
Conversion back T m(100％)	0.7675	0.7670	0.7650	0.7628	0.7620	0.7611	0.7588	0.7558

(4) consider that the spectrophotometer spectral width utilizes formula T to the influence of transmissivity in the transmission spectrum _M'=T _MAnd T _m'=T _m-(T _m* S/w _m) ²-(T _M* S/w _M) ²To extreme value transmissivity T _MAnd T _mRevise, obtain revised extreme value transmissivity T _M' and T _m', as shown in table 5.

The revised extreme value transmissivity of table 5 T _M' and T _m'

Wavelength (nm)	700	726	755	786	821	858	900	946
									Revise back T M′(100％)	0.8582	0.8585	0.8587	0.8589	0.8591	0.8594	0.8596	0.8598
Revise back T m′(100％)	0.7492	0.7512	0.7518	0.7519	0.7528	0.7535	0.7527	0.7510

(5) to revised extreme value transmissivity T _M' and T _m', utilize formula n ₁=[M+ (M ²-s ²) ^1/2] ^1/2With

$M=\frac{2s}{T_m^{\′}}-\frac{s^2+1}{2}$ Calculate the refractive index n of clear area and weak uptake zone ₁, as shown in table 6.

The refractive index n of table 6 clear area and weak uptake zone ₁

Wavelength (nm)	700	726	755	786	821	858	900	946
									Refractive index n 1	2.2644	2.2413	2.2235	2.2088	2.1948	2.1828	2.1761	2.1737

(6) utilize formula $m=\frac{{\mathrm{\λ}}_2}{2({\mathrm{\λ}}_2-{\mathrm{\λ}}_1)}$ Determine the pairing wave number m ' of transmissivity maximum value, differ the wave number m of half-integer 1/2 this characteristic correspondence when knowing all the other transmissivity extreme values by inference according to wave number between the adjacent extreme value; Then according to the wave number m and the refractive index n that obtain ₁, utilize transmissivity extremum conditions 2n ₁D=m λ obtains clear area and each extreme value wavelength film thickness d of weak uptake zone ₁Ask film thickness d at last ₁Arithmetic mean obtain the average thickness d=2..0647 μ m of film, as shown in table 7.

Give each extreme value wavelength film thickness d in the table 7 ₁With respect to the deviation of average thickness d, total mean deviation is 0.85.

The thickness and the deviation of table 7 GaN film

Wavelength (nm)	700	726	755	786	821	858	900	946
									Wave number m	13	12.5	12	11.5	11	10.5	10	9.5
The GaN thickness d 1(10 3nm)	2.0094	2.0245	2.0373	2.0461	2.0574	2.0637	2.0679	2.0672
									Thickness deviation (%)	1.82	1.08	0.46	0.03	0.52	0.83	1.04	1.0
Average thickness d d=2.0647 mean deviation 0.85%

(7), obtain the refractive index n of the film in the transmission spectrum scope, simultaneously to n with film average thickness d and wave number m substitution formula 2nd=m λ ₁Revise, the refractive index n of correction is as shown in table 8.

The refractive index n of table 8 clear area and weak uptake zone

Wavelength (nm)	700	726	755	786	821	858	900	946
									Refractive index n	2.2231	2.2170	2.2133	2.2082	2.2063	2.2009	2.1987	2.1955

Only provided the numerical value of wavelength GaN film refractive index when 700nm is above in the table 8, more to the numerical value of the GaN film in whole transmission spectrum scopes owing to data point, provide by Fig. 3.

(8) ask T _M' and T _m' geometrical mean $T=\sqrt{T_M^{\′}\×T_m^{\′}},$ With air and film, film and substrate, the reflection R between substrate and the air ₁=[(1-n)/(1+n)] ², R ₂=[(n-s)/(n+s)] ², R ₃=[(s-1)/(1+s)] ², utilize formula then

α＝-1/dln(1/B{A+[A ²+2BT(1-R ₂R ₃)] ^1/2}

Try to achieve absorption coefficient, in the formula

A＝-(1-R ₁)(1-R ₂)(1-R ₃)

B＝2T(R ₁R ₂+R ₁R ₃-2R ₁R ₂R ₃)

Because the data point that obtains is more, the result who obtains is provided by Fig. 4.

The thickness that has obtained the GaN film by top process is d=2.0647, and the mean deviation of the thickness that obtains is 0.85%, and Fig. 3 and Fig. 4 have provided the refractive index and the absorption coefficient of GaN film simultaneously.By Fig. 3 and Fig. 4 as can be known near the energy gap of GaN material, corresponding to about lambda1-wavelength 364nm, the refractive index n and the absorption coefficient of GaN material sharply increase, and along with the increase of lambda1-wavelength, the refractive index n trend of GaN material steadily, absorption coefficient goes to zero, and this rule meets the Changing Pattern of material refractive index n and absorption coefficient, has verified the feasibility of this method once more.

Above-mentioned embodiment is an an example of the present invention, and this method is not confined to the measurement to the GaN film, can realize measurement to other single side polishing substrate epitaxial film thickness and optical parametric with method of the present invention.

Claims (1)

1. the measuring method of single side polishing substrate epitaxial film thickness and optical parametric is the desirable epitaxial film thickness d of going out, epitaxial film refractive index n and epitaxial film absorption coefficient, and its concrete steps are as follows:

1) long epitaxial film on the single-sided polishing substrate is carried out the measurement of transmission spectrum, obtain transmission spectrum extreme value data T _{M surveys}And T _{M surveys}, and their pairing extreme value wavelength X _MAnd λ _m

2) according to the measurement result of step 1) in clear area and weak uptake zone to T _{M surveys}And T _{M surveys}Carry out Lagrange's interpolation and calculate, try to achieve pairing two the transmissivity extreme value T of each extreme value wavelength _{M is single}And T _{M is single}

3) according to formula $T_M=\frac{2s}{s^2+1}$ With known backing material refractive index s, draw the pairing theoretical transmissivity maximum value T of each extreme value wavelength _M

4) the transmissivity extreme value T to obtaining in the step 1) _{M is single}And T _{M is single}Carry out scaling, obtain the extreme value transmissivity T behind the scaling _MAnd T _m, this scaling coefficient is T _M/ T _{M is single}, the scaling formula is T _M=T _{M is single}* T _M/ T _{M is single}And T _m=T _{M is single}* T _M/ T _{M is single}

5) utilize formula T _M'=T _MAnd T _m'=T _m-(T _m* S/w _m) ²-(T _M* S/w _M) ²To the rate extreme value T behind the convergent-divergent _MAnd T _mRevise, obtain revised extreme value transmissivity T _M' and T _m', the width in the formula between two extreme value transmissivities is w _M=λ _{M (i-1)}-λ _{M (i+1)}And w _m=λ _{M (i-1)}-λ _{M (i+1)}, S is spectrophotometric spectral width;

6) to revised extreme value transmissivity T _m', utilize formula n ₁=[M+ (M ²-s ²) ^1/2] ^1/2And formula $M=\frac{2s}{T_m^{\′}}-\frac{s^2+1}{2}$ Draw the refractive index n of epitaxial film in clear area and weak uptake zone ₁

7) in the clear area of epitaxial film and weak uptake zone according to 1) in record two adjacent extreme value wavelength X of transmission spectrum ₁And λ ₂, utilize formula $m^{\′}=\frac{{\mathrm{\λ}}_2}{2({\mathrm{\λ}}_2-{\mathrm{\λ}}_1)}$ Determine the pairing wave number m ' of transmissivity maximum value, λ in the formula ₁Corresponding maximum value wavelength, λ ₂Corresponding minimal value wavelength and λ ₁＜λ ₂And differ half-integer 1/2 this characteristic according to wave number between the adjacent extreme value and know the pairing wave number m of all transmissivity extreme values by inference;

8) according to the wave number m and the refractive index n that obtain ₁, utilize transmissivity extremum conditions 2n ₁The film thickness d of correspondence when d=m λ draws clear area and weak uptake zone and the transmissivity extreme value occurs ₁, and to this thickness d ₁Carry out arithmetic mean and obtain the average thickness d of film;

9) utilize transmissivity extremum conditions 2nd=m λ and the film average thickness d and the wave number m that obtain, obtain the refractive index n of the film in the transmission spectrum scope, simultaneously to the refractive index n of film in clear area and weak uptake zone ₁Revise;

10) according to formula $T=\sqrt{T_M^{\′}\×T_m^{\′}}$ Draw revised extreme value transmissivity T in (5) _M' and T _m' geometrical mean, utilize simultaneously formula α=-1/dln (1/B{A+[A ²+ 2BT (1-R ₂R ₃)] ^1/2Try to achieve the absorption coefficient of film,

In the formula:

A＝-(1-R ₁)(1-R ₂)(1-R ₃)，

B＝2T(R ₁R ₂+R ₁R ₃-2R ₁R ₂R ₃)

R ₁, R ₂, R ₃Be air and film, film and substrate, the reflection coefficient between substrate and the air, and

R ₁＝[(1-n)/(1+n)] ²，R ₂＝[(n-s)/(n+s)] ²，R ₃＝[(s-1)/(1+s)] ²。