CN101609002B - New method for measuring optical band gap of semiconductor film material - Google Patents

Abstract

The invention belongs to the detection field of a semiconductor film, in particular to a method for measuring an optical band gap of a semiconductor film material. The method carries out spectrum unfolding analysis to transmission and reflection spectrum from result fitted angle, calculates accurate absorption coefficient and adopts a Tauc formula to calculate the accurate optical band gap on the basis of the accurate absorption coefficient. The method carries out strict calculating analysis and processing to the problems in the prior art, can eliminates the error caused by the two problems of the influence of the reflection of light in a film base system to the transmission and the influence of the absorption of a substrate to the transmission and leads the degree of accuracy of the optical band gap to be greatly improved.

Description

A kind of method of measuring optical band gap of semiconductor film material

Technical field

The invention belongs to the semiconductive thin film detection range, particularly a kind of new method of measuring optical band gap of semiconductor film material.

Background technology

When light was propagated in film, film caused the decay of light intensity to the absorption of light.Ignore under the condition of boundary reflection, the absorption coefficient of film and the pass of transmissivity are:

α(λ)＝-lnT(λ)/d

And the relation of absorption coefficient and optical band gap, available Tauc formulate is:

$Y={\left(\mathrm{\αh\ν}\right)}^{1/2}=A(\mathrm{h\ν}-E_g^{*})$

Therefore, utilize spectrophotometer measurement film based system transmissivity, can calculate the optical band gap of film.Current approach nearly all is based on this principle, but all there are following three problems in these methods:

1, do not consider that light is in the reflection of the film based system influence to transmission;

2, do not consider the influence of the absorption of substrate to transmission;

Because the existence of the problems referred to above, the absorption coefficient that the direct transmitance that obtains with test is calculated film will inevitably be introduced bigger error, and the optical band gap that this error can cause calculating produces than mistake.Therefore, how utilizing the transmission of sample and reflectance spectrum to obtain absorption coefficient accurately, is the important technological problems that the present invention will solve.

Summary of the invention

At the deficiencies in the prior art, the present invention separates analysis of spectrum from theoretical angle with experimental fit to transmission and reflectance spectrum, obtains absorption coefficient accurately, adopts the Tauc formula to obtain optical band gap accurately on this basis.The inventive method has been carried out strict computational analysis and processing to the existing in prior technology problem, can eliminate light in the reflection of film based system to the absorption of the influence of transmission and substrate this two errors that problem causes that influence to transmission, the order of accuarcy of optical band gap is significantly promoted.

A kind of method of measuring optical band gap of semiconductor film material of the present invention, its step comprises:

1, the at first reflection of blank testing substrate of glass and transmitted spectrum are obtained the optical parametric of substrate of glass, and described optical parametric comprises refractive index and the extinction coefficient of substrate of glass to the incident light of different wave length.

2, the reflection of test membrane based system and transmitted spectrum the optical parametric substitution reflection of substrate of glass or transmission equation, carry out curve fitting to the reflection or the transmitted spectrum of clear area, obtain film thickness.

3,, set up the equation with two unknowns group that concerns between reflectivity, transmissivity and the film refractive index of film based system and the extinction coefficient the reflectivity and the transmissivity equation of the refractive index of substrate of glass, extinction coefficient and film thickness substitution film based system.

The synoptic diagram that light transmits in the film based system when light incides film from air, reflects at film surface and film base interface as shown in Figure 1.Because film thickness and light wavelength differ and are not too big, therefore, interfere the reflectivity R of this process between the reflected light from film surface and film base interface _F1Be the result that each rank reflected light is interfered.In like manner, pass the light T at film base interface _I1Also be the result that each rank transmission is interfered, this process P ₁Expression.In film and substrate, exist the absorption of light to be respectively A _fAnd A _g

The light that passes film base interface will arrive substrate lower surface according to the direction of Snell law regulation, and a part is passed lower surface becomes transmitted light, and remainder is reflected back by lower surface, and repeatedly reflection and repeatedly transmission take place between interface and lower surface.Because the thickness of substrate is much larger than light wavelength, therefore, each rank transmitted light T ₁, T ₂, T ₃... between interference effect can ignore.

When the light that is reflected by substrate lower surface arrived film base interface, a part was reflected back toward substrate, and another part penetrates film and enters air, became second ingredient of the total reflection of film based system, used R _F2Expression.R _F2Being reverse transmissivity, is the result that repeatedly transmission is interfered.Reverse transmission process P ₂, P ₃... expression.P ₁, P ₂, P ₃... between separate, do not interfere.

Therefore, the total reflectivity of system and total transmittance are respectively:

R＝R _f1+AR _f2+BR _f3+... (1)

T＝T ₁+aT ₂+bT ₃+... (2)

Wherein A, B ... and a, b ... be the attenuation coefficient of light---luminous energy loss from front to back is more and more.Usually, energy has decayed to ten thousand/several magnitudes in the time of to C or c, and photometric measuring accuracy is about thousand parts several, is higher than photometric measuring accuracy, so counts on C or c gets final product.

Know that system always reflects and total transmission will be calculated A earlier _F1, A _F2..., A _G1, A _G2..., R ₁, R ₂... and T _I1, T _I2... and weight factor A, B ..., a, b ... wait intermediate variable, obtain R then _F1, R _F2... and T ₁, T ₂... wait reflection and transmitted component, respectively to reflection and transmitted component summation, obtain total reflectivity and total transmittance at last.

A _G1, A _G2..., R ₁, R ₂... and T ₁, T ₂... wait the computing formula of intermediate variable as follows:

$R_1=R_2=...=\left(\frac{1-n+\mathrm{ik}}{1+n-\mathrm{ik}}\right){\left(\frac{1-n+\mathrm{ik}}{1+n-\mathrm{ik}}\right)}^{*}---\left(3\right)$

T ₁＝T ₂＝...＝1-R ₁ (4)

A _g1＝A _g2＝...＝1-exp(-4πkt/λ) (5)

Calculate film based system eigenmatrix B, C value:

$\left[\begin{array}{c}B\\ C\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\δ}& i\sin \mathrm{\δ}/(n_1-{\mathrm{ik}}_1)\\ i(n_1-{\mathrm{ik}}_1)\sin \mathrm{\δ}& \cos \mathrm{\δ}\end{array}\right]\left[\begin{array}{c}1\\ n-\mathrm{ik}\end{array}\right]---\left(6\right)$

Wherein, δ=2 π (n ₁-ik ₁) dsin θ/λ is the phase thickness of film.The refractive index and extinction coefficient substitution (6) formula of the substrate of glass that step 1 is obtained, the expression formula of phase thickness in film thickness d substitution (6) formula that step 2 is obtained.

Then, calculate reflectivity R and transmissivity T:

$R=\left(\frac{{\mathrm{\η}}_{0}B-C}{{\mathrm{\η}}_{0}B+C}\right){\left(\frac{{\mathrm{\η}}_{0}B-C}{{\mathrm{\η}}_{0}B+C}\right)}^{*}---\left(7\right)$

$T=(1-R)\arctan \left(\frac{i{\mathrm{\η}}_0(B^{*}C-B{C}^{*})}{{\mathrm{\η}}_0^{2}B{B}^{*}-{\mathrm{CC}}^{*}}\right)---\left(8\right)$

According to energy conservation and in conjunction with above-mentioned formula, calculate A, B, C ... with a, b, c ... wait attenuation coefficient.

Can obtain the total reflectivity and the total transmittance of film based system in substitution formula 1 and the formula 2.

4, utilize theoretical spectral and test spectral fitting method, obtain the refractive index and the extinction coefficient of film, and then try to achieve the absorption coefficient of film.

The absolute value sum of deviation is the match deviation between definition matched curve and the measured curve:

$\mathrm{\η}=\underset{\mathrm{\λ}}{\mathrm{\Σ}}\left(\right|R-R_{\exp }|+|T-T_{\exp }\left|\right)---\left(9\right)$

Go into the film refractive index n of theoretical model the present age ₁With extinction coefficient k ₁With actual value near the time, match deviation η has minimum value.Therefore, find out minimum value and the corresponding n thereof of η ₁And k ₁, promptly found the refractive index and the extinction coefficient of film.

The pass of extinction coefficient k under the absorption coefficient of film and wavelength X and this wavelength is:

α＝4πk/λ (10)

5, obtain the absorption coefficient of film according to following formula, substitution Tauc formula is obtained the Y value then, according to the mapping of Y=f (hv) relation, linear fit is carried out in the better zone of linearity, can obtain the optical band gap of film.

Description of drawings

The synoptic diagram that Fig. 1 transmits in the film based system for light

Embodiment

Below by specific embodiment the present invention is further specified.

By reflection, the transmitted spectrum of reflection, transmitted spectrum and the film based system of blank substrate under the illumination of spectrophotometer test different wave length, the thickness t of substrate is a known parameters in the substrate explanation to operating personnel earlier.

According to the reflection of blank substrate, refractive index and the extinction coefficient that transmitted spectrum is calculated substrate, then according to formula (3), (4), (5) calculate light the reflectivity of glass air interface, light the transmissivity of glass air interface, light when penetrating film film to the absorptivity of light.

Calculate attenuation coefficients at different levels by formula (6) and in conjunction with law of conservation of energy, calculate each rank reflecting component R of film based system in substitution formula (7), (8) _F1, R _F2... with each rank transmitted component T _I1, T _I2...Calculate each rank according to A+R+T=1 and absorb component A _F1, A _F2...

Can obtain total reflectivity and total transmittance in substitution formula (1), (2).

Find the n of match deviation minimum value correspondence in the formula (9) ₁And k ₁Thereby, calculate the absorption coefficient of film, and according to the Tauc formulate:

$Y={\left(\mathrm{\αh\ν}\right)}^{1/2}=A(\mathrm{h\ν}-E_g^{*})$

Obtain the Y value.Above-mentioned whole calculating and fit procedure are finished by computing machine.

The corresponding Y value of the light hv of each different wave length, to the hv of all detections and corresponding Y value mapping thereof, match can obtain optical band gap accurately.This process can be carried out on Origin software.

Claims (3)

1. method of measuring optical band gap of semiconductor film material, its step comprises:

(1), the at first reflection and the transmitted spectrum of blank testing substrate of glass, obtain the optical parametric of substrate of glass, described optical parametric comprises refractive index and the extinction coefficient of substrate of glass to the incident light of different wave length;

(2), the reflection and the transmitted spectrum of test membrane based system, the optical parametric substitution reflection of substrate of glass or transmission equation, transmitted spectrum after the reflection of clear area is carried out curve fitting, obtain film thickness;

(3), the reflectivity and the transmissivity equation of the refractive index of substrate of glass, extinction coefficient and film thickness substitution film based system, utilize theoretical spectral and test spectral fitting method, obtain the refractive index and the extinction coefficient of film;

(4), calculate the absorption coefficient of film according to the extinction coefficient of film;

(5), the absorption coefficient substitution Tauc formula that obtains is obtained the Y value,, linear fit is carried out in the better zone of linearity, obtain the optical band gap of film according to the mapping of Y=f (hv) relation.

2. a kind of method of measuring optical band gap of semiconductor film material as claimed in claim 1 is characterized in that all described computation processes are finished on computers.

3. a kind of method of measuring optical band gap of semiconductor film material as claimed in claim 1 is characterized in that, the described test process of described step 1 and step 2 uses spectrophotometer to test.