CN1063159A - Measure the new method of semiconductor nonequilibrium carrier lifetime - Google Patents

Abstract

The invention provides a kind of new method of measuring the semiconductor nonequilibrium carrier lifetime.Be in semiconductor, to excite free carrier with the light method for implanting, the frequency location on mobile reflectance spectrum reflection limit, thus the incident light of another bundle frequency on the reflection limit changed significantly at the reflectivity of semiconductor surface.Utilize this method to measure the life-span of nonequilibrium carrier in the semiconductor, not only do not have strict demand, and be not damaged, non-cpntact measurement, can study the carrier lifetime under the various energy state, homogeneity that more can sample for reference making sample.

Description

Measure the new method of semiconductor nonequilibrium carrier lifetime

The invention belongs to the measuring method of the nonequilibrium carrier lifetime in the field, particularly a kind of semiconductor material of using infrared ray, visible light research or analysis of material.

Existing measurement method of life all is based on the photoconductivity decay principle mostly.Using maximum is the photoconductivity decay method.The similar photoconductive device of specimen in use also will be done electrode.Changed into afterwards with the microwave measurement and followed photo-generated carrier and the electricity that increases is led, sample is placed in the microwave cavity, transmission beam method is arranged, reflectometry is also arranged, and the measurement result of microwave method is consistent with the photoconductivity decay method, but this method experimental facilities is still complicated, and insufficient sensitivity, for the ease of observation signal, light beam is gone into often stronger, and the charge carrier that is injected into is filled into very high state in being with.But the function of the energy of nonequilibrium carrier lifetime is the large-signal life-span so existing method records, rather than small-signal life-span of needing of photoelectric device.The microwave reflection reference is: M.C.Chen, Photconductivity life time measurements on HgCdTe using a contact less microwave technique, Journal of Applied Physics, Vol.64.945(1988).

The method that the purpose of this invention is to provide a kind of new measurement semiconductor nonequilibrium carrier lifetime.Not only the making of sample is not had strict demand, and can study the carrier lifetime under the various energy state, homogeneity that more can sample for reference.Can be as new experimental technique about nonequilibrium carrier relaxation process fundamental research in the semiconductor, the new means that can identify as semiconductor material again.

As everyone knows, semi-conductive infrared reflectance spectrum R(ω) can describe with the vibrator model of classics, be example with the n type material:

$R\left(\mathrm{\ω}\right)=\frac{{(n-1)}^2+k^2}{{(n+1)}^2+k^2}\left(1\right)$

$E\left(\mathrm{\&omega;}\right)={(n+\mathrm{ik})}^2={\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="921083122\_DRIMG1.png,921083122\_DRIMG5.png"\; state="\{\{state\}\}">E</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="iE"\; filenames="921083122\_DRIMG1.png,921083122\_DRIMG4.png"\; state="\{\{state\}\}">iE</figure-callout>}}_2=E_{\&infin;}+\underset{j}{\mathrm{\&Sigma;}}\frac{{\mathrm{Sj\&omega;}}^{2}j}{{\mathrm{\&omega;}}_j^2-{\mathrm{\&omega;}}^2-\mathrm{i\&Gamma;j\&omega;}}-\frac{E_{\&infin;}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="921083122\_DRIMG1.png,921083122\_DRIMG4.png"\; state="\{\{state\}\}">P</figure-callout>}}^2}{{\mathrm{\&omega;}}^2+{\mathrm{iy}}_p\mathrm{\&omega;}}\left(2\right)$ ${\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="921083122\_DRIMG1.png,921083122\_DRIMG4.png"\; state="\{\{state\}\}">p</figure-callout>}}^2=\frac{4\mathrm{\&pi;Ne}{e}^2}{E_{\&infin;}{\mathrm{<figure-callout\; id="5"\; label="m"\; filenames="921083122\_DRIMG2.png,921083122\_DRIMG3.png"\; state="\{\{state\}\}">m</figure-callout>}}_5^{*}}\left(3\right)$

Wherein n and k are respectively refractive index and extinction coefficient, E ₁And E ₂Be dielectric function E(ω) real part and imaginary part, E _∞Be the contribution of all interband transition items, ω j, Sj and Г j are oscillator frequency, intensity and damping, and ω p and γ p are plasma frequency and damping, and Ne is an electron concentration, and e is an electron charge, m ^* _sBe electron effective mass can be with mean value.Obviously reflectance spectrum is relevant with ω p, also relevant with Ne certainly.

Following elder generation does an explanation to accompanying drawing of the present invention.

Fig. 1 is two reflectance spectrums of certain semiconductor samples, and being characterized in has a reflectivity minimum at low frequency end, herein E ₁=1.When frequency reduced again, reflectivity sharply rose, until near total reflection, this moment E ₁=0.We are 0＜E ₁＜1 interval interior reflectance spectrum is called the reflection limit.The Ne of figure mid point 2 places spectrum is slightly larger than the some spectrum at 1 place.Be provided with irradiating laser and shine on the sample, its photon frequency ω is just in time in point 1 frequency of living in, and at this moment reflectivity is provided by point 1 place, is about 30%, establishes this moment sample again and is subjected to certain unexpected external excitation beam and excites, and its carrier concentration Ne is increased.Because intrinsic carrier relaxation process just reaches new numerical value through one section by Ne after the time of life-span sign.Meanwhile, reflectance spectrum also develops into new spectrum, promptly puts 2 residing spectrums, and sample just provides about 60% by point 2 to the reflection of incident light rate.If external excitation beam suddenly disappears, Ne becomes original numerical value again after after a while, and reflectance spectrum also becomes old spectrum by new spectrum naturally.Reflectivity returns to original numerical value again.This as seen from Figure 1 periodic process, obviously the information that has comprised the nonequilibrium carrier relaxation process in the reflective light intensity 4, moving of its reflectance spectrum by 3 expressions, further, measure the relaxation process between two adjacent in the exciting of a series of strength decreases excitation intensities successively, the relaxation time that just can study from the high-energy state to the low-energy state changes.

Fig. 2 is a measuring process illumination synoptic diagram, and 5 is illuminating laser beams among the figure, the 6th, and excitation beam, the 7th, reflected light laser beam.

Fig. 3 is the Hg to 77K _0.8Cd _0.2The relaxation process of the reflectance varies of the calculating gained of Te sample.

Fig. 4 is excitation beam 6 irradiation times or the Hg to 77K during less than the life-span _0.8Cd _0.2The Te sample calculates the relaxation process of the reflectance varies of gained.

Fig. 5 is the amplitude of alternation composition of reflectivity among Fig. 4 and the relation of excitation beam irradiation time.Curve among the figure is at the 100th periodicity of illumination result of calculation.

Below in conjunction with accompanying drawing the present invention is elaborated.

The invention provides a kind of method of measuring the semiconductor nonequilibrium carrier lifetime, the steps include:

At first, prepare excitation beam 6 and remove to shine sample with excitation beam 6, excitation beam 6 has two or more strength grades, can in semiconductor, produce photo-generated carrier, the photoproduction carrier concentration that the basis of design of its intensity at different levels is required and deciding, the intensity of excitation beam 6 can be switched between adjacent two intensity successively, and switching time should be much smaller than carrier lifetime.

Utilize the minimal value of reflectance spectrum to determine photoproduction carrier concentration Ne again; Remove to shine sample with known illuminating laser beam 5, and measure the intensity of its reflection lasering beam 7, shine samples and adjust its intensity with excitation beam 6 simultaneously, utilize the position on the increase and decrease of the photoproduction carrier concentration reflection limit on can mobile reflectance spectrum, if the intensity of excitation beam 6 reaches at 1 o'clock, reflect the minimum frequency that moves to illuminating laser beam 5, at this moment the intensity minimum of reflection lasering beam 7, the frequency of illuminating laser beam 5 promptly reflects minimum frequencies omega min, also is the position of dR/d ω=0.Here R is a reflectivity, and ω is a frequency.For semiconductor commonly used, as mercury cadmium telluride, indium antimonide, indium arsenide, gallium arsenide, E _∞With the oscillator parameter all be known, (2) unknown parameter has only ω p and γ p in the formula, can calculate plasma frequency ω p and plasma damping γ p according to (1) to (3) formula like this, when reflecting minimum frequencies omega min much larger than the oscillator frequency, the reflection minimal value approaches zero, obtains plasma frequency ω p with approximate expression:

ω ²p＝ω ²min（1-1/E _DO） （4）

Because (3) Ne in the formula and m ^* _sAll be the function of Fermi level Ef, calculate Ef from ω p, obtain Ef, can calculate Ne, suppose Ne=N this moment by successive iteration method.In like manner, if remove to shine sample, when excitation beam intensity reaches l with the slightly high illuminating laser beam 5 of another photon frequency _oDuring+ls, it is minimum to reappear reflection, and can calculate Ne=N _o+ Ns.

The intensity of supposition excitation beam 6 is at l now _oAnd l _oSuddenly shear between+ls:

Then photoproduction carrier concentration Ne is provided by following formula:

(5) show that with (6) formula when excitation beam 6 light intensity switched to adjacent higher-strength by an intensity suddenly, photoproduction carrier concentration increased in relaxation process, the corresponding growth of the light intensity of reflection lasering beam 7 is also synchronously moved on the reflection limit to high frequency direction; Because the response time of photovoltaic detector is shorter than the life-span of nonequilibrium carrier in the material,, after amplifying, broad band amplifier on oscillograph, shows and storage so the light intensity that available photovoltaic detector goes to receive folded light beam 7 changes; When excitation beam 6 returned lower intensity suddenly, photoproduction carrier concentration was decayed in relaxation process, and this inverse process also shows storage on oscillograph.

Then, carrier concentration substitution (3) to (1) formula that (6) formula is provided is tried to achieve τ thereby τ gone time of the intensity of the reflection lasering beam 7 that stores on the match oscillograph change as adjustable parameter.

In (5) and (6) formula, N _oWith Ns be corresponding to light intensity l _oWith the photoproduction carrier concentration of ls, T is the irradiation time.

As an example, Fig. 3 is to the Hg under the 77K _0.8Cd _0.2The result of calculation of Te sample.Used oscillator parameter is taken from the fitting result to the actual measurement reflectance spectrum, lists in table 1.Other parameter is: γ p=10 centimetre ^-1, E _∞=12.6 also take from fitting result.Excitation beam 6 has been got four intensity in the calculating, and these four intensity can make sample that the reflection of four irradiating lasers is reached minimum respectively, and the methyl alcohol laser instrument has the strongest output in these four frequencies.Listed these Wavelength of Laser in the table 2 and, also had the relative carrier concentration between each excitation intensity from reflecting the minimum ω p that calculates.Curve 8 among Fig. 3 is the relaxation curves that excite between second intensity to the first intensity.Curve 9 is the relaxation processes that excite between the 3rd intensity to the first intensity.Curve 10 is the relaxation curves that excite between top four's degree to the first intensity.Remove match actual measurement relaxation curve with these curves, just can try to achieve the life-span τ in the corresponding relaxation process.

Table 1, Hg during 77K _0.8Cd _0.2The oscillator parameter of Te

The oscillator frequencies omega (centimetre ^-1) the strength S damping " (centimetre ^-1)

1 154.86 0.211 8.05

2 125.27 3.27 6.2

3 110.26 0.54 7.6

ω p and relative carrier concentration when four laser frequencies the strongest of table 2 methyl alcohol laser instrument and sample reach minimal value to the reflection of these four laser

The sequence of intensity laser frequency (centimetre ^-1) ω p(centimetre ^-1) relative concentration

1 61.3 68 1

2 84.2 100 1.162

3 175.4 125 2.379

4 214.1 184 6.321

The design of said excitation beam 7 among the present invention also can be to make laser intensity be stabilized in end illumination, removes to shine sample with the consistent or inconsistent fill-in light with end illumination of another bundle frequency and produces photoproduction carrier concentration Ns.

The alternation composition of said excitation beam 6 can be the cycle or aperiodic, can be rectangle or the triangle wave mode, or sinusoidal, or the modulation light intensity of ladder type.

Said excitation beam 6 can be a visible or infrared light, also can be coherent light or incoherent light.

The intensity of said excitation beam 6 has the intensity of a series of alternations, measures between adjacent two light intensity of intensity alternation successively, can try to achieve the life-span between adjacent two concentration in a series of photoproduction carrier concentration alternation processes.

The said measurement of the present invention can be to adopt the light beam that focuses on to carry out, or non-focusing light beam be carried out.Said measurement is that the point of fixity to sample surfaces carries out, or more is applicable to the sample for reference homogeneity at the sample surfaces scanning survey.

The said sample of the present invention can be lift a ban band or other bandgap semiconductor material or membraneous material.

If measuring system can't show and store reflected light beam signal as shown in Figure 3, then can select another measuring method.Promptly periodically switch excitation beam 6, make l _oAnd l _oThe residence time of+ls state all is T, when time T is equal to or less than life-span τ, the relaxation of photo-generated carrier makes its variation not catch up with the variation of excitation light intensity, see also Fig. 4, curve 11 is that excitation beam second intensity is to the relaxation curve between first intensity, its T/ τ=0.2. curve 12 be excitation beam the 3rd intensity to the relaxation curve between first intensity, its T/ τ=0.5.Curve 13 is the relaxation curves between excitation beam top four degree to the first intensity, its T/ τ=1.0.The amplitude △ R of the Alternating Component of reflective light intensity is illustrated among Fig. 5, and curve is to calculate and get at the 100th periodicity of illumination among Fig. 5. Curve 14,15,16 corresponds respectively to the relaxation process of curve 11,12,13 among Fig. 4.As shown in Figure 4, progressively shorten time T, amplify the signal of f=1/2T with the frequency-selecting amplifier of centre frequency, can get similar curve shown in Figure 5, as adjustable parameter, this is measured the curve ratio calculated among curve and Fig. 5 with τ, from the two match of being satisfied with, try to achieve life-span τ.

The present invention has following good effect and advantage: the method that the present invention proposes is not high to sample requirement, is the not damaged non-cpntact measurement.Can measure nonequilibrium carrier lifetime in any photodetection modulator material, also can study charge carrier in being with from high-energy state to low-energy state relaxation process progressively.If adopt defocused laser beam in sample surfaces synchronous scanning, all right sample for reference homogeneity, measuring method is simpler than microwave measurement, especially at low temperatures, the light inlet window on the chamber wall.Just can introduce light beam, it is much then complicated to introduce microbeam.

Claims (8)

1, a kind of method of measuring the semiconductor nonequilibrium carrier lifetime is characterized in that:

A. prepare excitation beam 6 and remove to shine sample with excitation beam 6; Excitation beam 6 has two or more strength grades, can in semiconductor, produce photo-generated carrier, the photoproduction carrier concentration that the basis of design of its intensity at different levels is required and deciding, the intensity of excitation beam 6 can be switched between adjacent two intensity successively, and switching time should be much smaller than carrier lifetime;

B. utilize the minimal value of reflectance spectrum to determine photoproduction carrier concentration Ne; Remove to shine sample with known illuminating laser beam 5, and measure the light intensity of its reflection lasering beam 7, shine samples and adjust its intensity with excitation beam 6 simultaneously, utilize the increase and decrease of photoproduction carrier concentration can be mobile the position on reflectance spectrum reflection limit, with the minimum frequency that moves to illuminating laser beam 5 of reflection, this moment reflection lasering beam 7 the intensity minimum, the frequency of illuminating laser beam 5 promptly reflects minimum frequencies omega min, also be the position of dR/d ω=0, can calculate plasma frequency ω p and plasma damping γ p according to following (1) to (3) formula like this:

$R\left(\mathrm{\&omega;}\right)=\frac{{(n-1)}^2+k^2}{{(n+1)}^2+k^2}\left(1\right)$ $E\left(\mathrm{\&omega;}\right)={(n+\mathrm{ik})}^2=E_1+{\mathrm{iE}}_2=E_{\&infin;}+\underset{j}{\mathrm{\&Sigma;}}\frac{{\mathrm{Sj\&omega;}}^{2}j}{{\mathrm{\&omega;}}_j^2-{\mathrm{\&omega;}}^2-\mathrm{i\&Gamma;j\&omega;}}-\frac{E_{\&infin;}{\mathrm{\&omega;}}_P^2}{{\mathrm{\&omega;}}^2+{\mathrm{iy}}_p\mathrm{\&omega;}}----\left(2\right)$ ${\mathrm{\&omega;}}_p^2=\frac{4\mathrm{\&pi;Ne}{e}^2}{E_{\&infin;}{m}_5^{*}}\left(3\right)$

When reflecting minimum frequencies omega min much larger than the oscillator frequency, the reflection minimal value approaches zero, obtains plasma frequency ω p with approximate expression:

ω ²p=ω ²min(1-1/E _∞) (4)

Because (3) Ne in the formula and m ^* ₃All be the function of Fermi level Ef, calculate Ef from ω p, obtain Ef, can calculate Ne by successive iteration method;

N and k are respectively refractive index and extinction coefficient in the formula, E ₁And E ₂Be real part and the imaginary part of dielectric function E (ω), E _∞Be the contribution of all interband transition items, ω j, Sj and τ j are oscillator frequency, intensity and damping, and ω p, γ p are plasma frequency and damping, and Ne is an electron concentration, and e is an electron charge, m ^* ₃Be electron effective mass can be with mean value;

C. indicate the relaxation process of nonequilibrium carrier with the light intensity change procedure of reflection lasering beam 7; Because the reflection limit is very steep, when excitation beam 6 light intensity switched to adjacent higher intensity by an intensity suddenly, photoproduction carrier concentration increased in relaxation process, and the corresponding growth of the light intensity of reflection lasering beam 7 is also synchronously moved on the reflection limit to high frequency direction; The light intensity of going to receive folded light beam 7 with photovoltaic detector changes, and shows on oscillograph after amplifying and deposits storage; When excitation beam 6 returned lower intensity suddenly, inverse process also showed storage on oscillograph;

D. life-span τ is tried to achieve in the variation of the time of the intensity of the reflection lasering beam 7 that stores on the match oscillograph; If the light intensity of the excitation beam 6 between two adjacent light intensity is provided by following formula:

Then photoproduction carrier concentration Ne is provided by following formula:

With this Ne numerical value substitution (1) to (3) formula, τ is used as parameter, calculates the Strength Changes of reflection lasering beam 7, with the intensity match of the reflector laser that stores on the oscillograph, and adjusting τ till obtaining the most satisfied match, the τ of this moment is the life-span of the semiconductor nonequilibrium carrier asked.

In (5) and (6) formula, N and NS are the photoproduction carrier concentration corresponding to light intensity I and Is, and T is the irradiation time, and t is a time variable.

2, the method for measurement semiconductor nonequilibrium carrier lifetime according to claim 1, the design that it is characterized in that said excitation beam 6 is to make laser intensity be stabilized in end illumination, removes to shine sample with the consistent or inconsistent fill-in light with end illumination of another bundle frequency and produces photoproduction carrier concentration Ns.

3, according to the method for the measurement semiconductor nonequilibrium carrier lifetime of claim 1 defined, the alternation composition that it is characterized in that said excitation beam 6 is the cycle or aperiodic, and is rectangle or leg-of-mutton, or sinusoidal, or the modulation light intensity of ladder type.

4, the method for measurement semiconductor nonequilibrium carrier lifetime according to claim 1 is characterized in that said excitation beam 6 is visible or infrared lights, is coherent light or incoherent light.

5, the method for measurement semiconductor nonequilibrium carrier lifetime according to claim 1, it is characterized in that the intensity of said excitation beam 6 has the intensity of a series of alternations, between adjacent two light intensity of intensity alternation, measure successively, try to achieve the life-span between adjacent two concentration in a series of photoproduction carrier concentration alternation processes.

6, the method for life of measurement semiconductor nonequilibrium carrier according to claim 1 is characterized in that said measurement is that employing focuses on or non-focusing light beam carries out.

7, the method for life of measurement semiconductor nonequilibrium carrier according to claim 1 is characterized in that said measurement is that point of fixity to sample surfaces carries out, or carries out in sample surfaces scanning.

8, the method for measurement semiconductor nonequilibrium carrier lifetime according to claim 1 is characterized in that said sample is lift a ban band or other bandgap semiconductor material or membraneous material.

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