CN100559168C - A Method for Measuring the Size Distribution of Semiconductor Quantum Dots Using Fluorescence Spectroscopy - Google Patents

Abstract

The invention discloses a method for measuring the size distribution of semiconductor quantum dots by using fluorescence spectrum. This method measures the PL spectrum of the semiconductor multi-quantum dot system; starting from the time-dependent perturbation Schrödinger equation under the effective mass approximation, calculates the PL spectrum of the semiconductor multi-quantum dot; and then obtains the size of the quantum dot by comparing the theoretical and experimental PL spectra Distribution, where the central wavelength of the PL spectrum corresponds to the composite luminescence of quantum dots with the largest proportion, and the shape of the PL spectrum corresponds to the distribution of the size. The invention has simple operation and short time consumption; the size distribution of the semiconductor multi-quantum dot system can be clearly obtained.

Description

A Method for Measuring the Size Distribution of Semiconductor Quantum Dots Using Fluorescence Spectroscopy

technical field

The invention relates to a method for measuring the size distribution of InAs/GaAs or InAs/InP semiconductor quantum dots by using fluorescence spectrum.

Background technique

The self-organized growth mode is currently the more commonly used quantum dot growth method. In practical device applications, in order to optimize the performance of optoelectronic devices such as quantum dot lasers and quantum dot detectors, a high-density multi-layer multi-quantum dot system growth method is generally used. Because this method is difficult to grow a multi-quantum dot system with uniform size, the PL spectrum of quantum dots does not show the characteristics of delta function, but shows a certain broadening, which hinders the application of quantum dot optoelectronic devices to a certain extent. performance. For this reason, some people use different orientations and patterned substrates and optimize the growth process, which improves the uniformity of quantum dots to a certain extent, but the results are still not ideal. It is more directional and forward-looking to directly guide the production process by detecting the uniformity of the size distribution of InAs/GaAs or InAs/InP semiconductor quantum dots. At present, the commonly used detection methods include atomic force microscope, high-resolution transmission electron microscope, etc. The disadvantage of these methods is that the detection process is complicated. Since the application of quantum dot materials focuses on the photoelectric properties, the fluorescence (PL) spectrum is more directly related to the photoelectric properties. The size distribution of InP quantum dots will be a better detection method.

Contents of the invention

The purpose of the present invention is to propose a PL spectrum of InAs/GaAs or InAs/InP multi-quantum dot system through actual measurement and theoretical calculation, combined with analytical methods to obtain the distribution of InAs/GaAs or InAs/InP semiconductor quantum dot size.

Utilize fluorescence spectrum of the present invention to measure InAs/GaAs or the method for InAs/InP semiconductor quantum dot size distribution as follows:

1). Measurement of PL spectrum of InAs/GaAs or InAs/InP semiconductor quantum dots

The quantum dot sample is placed under the objective lens of the microfluorescence spectrometer, the measurement temperature is controlled below 270K, the incident laser wavelength is 632.8nm, and the excitation power is 10-750mW. At this time, the carrier concentration generated in the quantum dot sample is 1.0 ×10 ¹⁶ -1.0×10 ¹⁷ cm ^-3 , thus measuring the PL spectrum of the quantum dot sample.

2). Theoretical calculation of PL spectrum of semiconductor quantum dots

Under the approximation of the effective mass and hemispherical quantum dots, the quantum dots are assumed to have a Gaussian size distribution, and the time-dependent Schrödinger equation is solved using Fortran software:

表示对所有量子点体积积分后计算得到的理论模拟PL谱，

其中ω和E分别为普朗克常量、光波频率和光子能量。In the formula, Nc(V) is the carrier concentration in the quantum dot when the volume of the quantum dot is V, wherein the carrier concentration Nc(V) in the quantum dot is proportional to its volume, that is, Nc(V)∝V; The luminescence spectrum corresponding to the volume of quantum dots is V; S(V) is the Gaussian distribution of quantum dots, $S\left(V\right)=\exp (-\frac{{(\sqrt[3]{V}-\sqrt[3]{V_0})}^2}{2{\left(\mathrm{\σ}\sqrt[3]{V_0}\right)}^2}),$ V ₀ is the volume of the quantum dot corresponding to the peak of the PL spectrum, σ is the separation variable,

Indicates the theoretically simulated PL spectrum calculated after volume integration of all quantum dots,

in ω and E are Planck's constant, light wave frequency and photon energy, respectively.

3). From the formula (1), it can be seen that the peak and broadening changes of the PL spectrum are only related to V ₀ and σ. Therefore, first assume that V ₀ and σ are any two values greater than zero (V ₀₁ , σ ₁ ) to calculate PL spectrum, and compared with the PL spectrum measured in the experiment. If the calculated peak energy (E ₁ ) of the PL spectrum is less than the experimentally measured peak energy (E ₀ ), then V ₀₁ is reduced until the calculated peak energy (E ₂ ) of the PL spectrum is greater than the experimentally measured The peak energy of PL (E ₀ ), and the corresponding volume is V ₀₂ . Conversely, if E ₁ >E ₀ , increase V ₀₁ so that the calculated peak energy (E ₂ ) of the corresponding PL spectrum is smaller than the experimentally measured PL peak energy (E ₀ ). In this way, the central dimension V ₀ of the quantum dot is between V ₀₁ and V ₀₂ . Then, the central size V _{0 tone} is obtained by using the dichotomy method, so that the peak energy E of the PL spectrum corresponding to the V _{0 tone} satisfies |E ₀ −E|<=0.001. At this time, it is considered that V ₀ =V _{0 is tuned} .

4). Keeping V ₀ unchanged, calculate the PL spectrum corresponding to (V _{0 tone} , σ ₁ ), and compare it with the half-width of the PL spectrum measured in the experiment. If the calculated half-width of the PL spectrum is greater than the experimental PL The half-peak width of the spectrum makes σ ₁ smaller until the calculated half-width of the PL spectrum is smaller than the half-width of the experimental PL spectrum. At this time, the corresponding size separation variable is σ ₂ . Conversely, if the calculated half-peak width of the PL spectrum < the half-peak width of the experimental PL spectrum, then make _σ1 larger until the calculated half-peak width of the PL spectrum > the half-peak width of the experimental PL spectrum, then the corresponding size separation variable is σ ₂ . In this way, the central size σ of the quantum dot is between σ ₁ and σ ₂ . Finally, the size separation variable σ _tone is obtained by using the dichotomy method, so that the half-width energy of the PL spectrum corresponding to the σ _tone satisfies |E _{0 half} -E|<=0.001, then we consider σ=σ _tone .

5). At this time, the size distribution of quantum dots is:

The present invention is based on the fact that quantum dots with different sizes have different abilities to capture carriers, thus making different contributions to recombination luminescence. Under a certain excitation power, although large-sized quantum dots have more carrier injections, since the large-sized quantum dots account for a small proportion in the entire quantum dot system, the PL spectrum of the quantum dot system contribution is small. Quantum dots, which account for the vast majority of size distribution, contribute the most to the PL spectrum of the quantum dot system due to their absolute advantage in number, showing that the peak of the PL spectrum corresponds to the composite luminescence of quantum dots of this size. The half-width of the PL spectrum of the quantum dot system is due to the broadening of the spectral line caused by the size distribution of the quantum dots. Therefore, the size distribution of quantum dots can be obtained by comparing the theoretical PL spectrum with the experimentally measured PL spectrum.

The method of the invention is simple in operation, short in time consumption, clear in judging criteria, and can predict the luminous performance of the quantum dot system, facilitates grading treatment of semiconductor quantum dot material products, and facilitates upgrading of product quality.

Description of drawings

Figure 1 shows the measured PL spectrum (solid line) of the InAs/GaAs multi-quantum dot system when the measurement temperature is 80K and the corresponding PL spectrum (dotted line and dashed line) when the size separation variable (σ) is 0.09 and 0.07 according to the theoretical calculation ).

Figure 2 is the quantum dot size distribution figure measured by atomic force microscope, (a) figure is the distribution figure of the measured quantum dot; (b) the bar graph in the figure is the actual size distribution of statistical quantum dots, and the dotted line is Gaussian Size distribution of quantum dots under approximation.

Fig. 3 keeps the size separation variable σ=0.04 unchanged, makes V ₀₁ =530nm ³ and V ₀₂ =790nm ³ , uses the dichotomy method for spectral comparison to find the spectral demonstration diagram of the central size V ₀ of quantum dots.

Fig. 4 is a spectrum demonstration diagram of finding the central separation variable σ of the quantum dots by using the dichotomy method for spectral comparison while keeping the central size V ₀ =730nm ³ unchanged, making σ ₁ =0.04 and σ ₂ =0.1.

Detailed ways

Below by embodiment and accompanying drawing, the present invention is described in further detail:

1. In this embodiment, InAs/GaAs quantum dot samples are used, and the PL spectrum is first measured, and the measurement conditions are:

The quantum dot sample is placed under the objective lens of the microfluorescence spectrometer, the measurement temperature is controlled at a low temperature of 80K, the incident laser power is 200mW, and the incident laser wavelength is 632.8nm. At this time, the carrier density formed in the quantum dot sample is about 1.6×10 ¹⁶ cm ^-3 , and the PL spectrum of the InAs/GaAs quantum dot system is measured, as shown in the solid line in Figure 1, where the center of the peak of the PL spectrum can be seen The position (E ₀ ) is 1.24eV, and the half width is 75meV.

2. Calculate the PL spectrum of the system according to the above-mentioned theoretical calculation method of InAs/GaAs semiconductor quantum dot PL spectrum:

First set V ₀ and σ as any two values greater than zero, and use Fortran software to calculate the PL spectrum. It is found that when σ=0.04, V ₀₁ =530nm ³ , the half-peak width of the calculated PL spectrum is less than 75meV, and the peak The center position E ₁ is greater than 1.24eV, satisfying E ₁ >E ₀ . Then keep σ=0.04 unchanged, and select another V ₀₂ >530nm ³ , so that the corresponding peak of the PL spectrum satisfies E ₂ <E ₀ , and it is found that the PL spectrum calculated when V ₀₂ =790nm ³ satisfies this condition. Then, the central dimension V ₀ =730nm ³ of the quantum dot is found by the dichotomy method. At this time, the center position of the calculated PL spectrum corresponds to the center position 1.24eV of the experimentally measured spectral line.

3. Keep the central dimension V ₀ =730nm ³ of the quantum dots unchanged. It is known that the half-peak width of the PL spectrum calculated when σ ₁ =0.04 is less than 75meV. At this time, a larger size separation variable is selected to make the calculated half-peak width of the PL spectrum greater than 75meV. It is found that when σ ₂ =0.1 meet that requirement. Spectral comparison using the dichotomy method finds the size separation variable σ=0.07 of the quantum dots.

At this time, the size distribution S(V) of quantum dots can be calculated by the formula $S\left(V\right)=\exp (-\frac{{(\sqrt[3]{V}-\sqrt[3]{730})}^2}{2{\left(0.07\sqrt[3]{730}\right)}^2})$ to express. When σ=0.07, V ₀ =730nm ³ , the spectral line matches the experiment best, see the dotted line in Fig. 1 . And this is very close to the size separation variable σ=0.09 measured directly by atomic force microscope, as shown in the dotted line in Fig. 2(b).

The size distribution of quantum dots is different, the measured and calculated PL peaks and shapes are different, and the PL spectrum corresponding to a size distribution is unique, so our method can effectively find the size distribution of quantum dots.

The above-described embodiments are only to illustrate the technical ideas and characteristics of the present invention, and its purpose is to enable those of ordinary skill in the art to understand the content of the present invention and implement it accordingly. The scope of this patent is not limited to the above-mentioned specific embodiments. , that is, all equivalent changes or modifications made according to the spirit disclosed in the present invention are still covered by the protection scope of the present invention.

Claims (1)

1. a method utilizing fluorescence spectrum to measure InAs/GaAs semiconductor quantum dot size distribution, is characterized in that concrete steps are as follows: §A. Measurement of PL spectrum of semiconductor quantum dots The quantum dot sample is placed under the objective lens of the microfluorescence spectrometer, the measurement temperature is controlled below 270K, the incident laser wavelength is 632.8nm, and the excitation power is 10-750mW, and the PL spectrum of the quantum dot sample is measured; §B. Theoretical Calculation of PL Spectrum of Semiconductor Quantum Dots Under the approximation of the effective mass and hemispherical quantum dots, the quantum dots are assumed to have a Gaussian size distribution, and the time-dependent Schrödinger equation is solved using Fortran software:

In the formula, Nc(V) is the carrier concentration in the quantum dot when the volume of the quantum dot is V, wherein the carrier concentration Nc(V) in the quantum dot is proportional to its volume, that is, Nc(V)∝V; The luminescence spectrum corresponding to the volume of quantum dots is V; S(V) is the Gaussian distribution of quantum dots, $S\left(V\right)=\exp (-\frac{{(\sqrt[3]{V}-\sqrt[3]{V_0})}^2}{2{\left(\mathrm{\&sigma;}\sqrt[3]{V_0}\right)}^2}),$ V ₀ is the volume of the quantum dot corresponding to the peak value of the PL spectrum, and σ is the separation variable; represents the theoretically simulated PL spectrum calculated after volume integration over all quantum dots, in

ω and E are Planck's constant, light wave frequency and photon energy, respectively; §C. From the formula (1), it can be seen that the peak and broadening changes of the PL spectrum are only related to V ₀ and σ. Therefore, assuming that V ₀ and σ are any two values greater than zero, V ₀₁ and σ ₁ , calculate the PL Spectrum, and compared with the experimentally measured PL spectrum, if the calculated peak energy E ₁ of the PL spectrum is less than the experimentally measured PL peak energy E ₀ , then V ₀₁ is reduced until the calculated PL spectrum is The peak energy E ₂ is greater than the experimentally measured PL peak energy E ₀ , and the corresponding volume is V ₀₂ ; on the contrary, if E ₁ > E ₀ , increase V ₀₁ to calculate the corresponding peak energy of the PL spectrum E ₂ is smaller than the peak energy E ₀ of the PL measured experimentally, and the central dimension V ₀ of the quantum dot is between V ₀₁ and V ₀₂ ; then, the central dimension V _{0 tune} is obtained by using the dichotomy method, so that the V _{0 tune} corresponds to the PL The peak energy E of the spectrum satisfies |E ₀ -E|<=0.001, V ₀ =V _{0 tuning} ; §D. Keep V ₀ unchanged, calculate the PL spectrum corresponding to V _{0 tone} , σ ₁ , and compare it with the experimentally measured PL spectrum half-width, if the calculated PL spectrum half-width is greater than the experimental PL spectrum half-width peak width, then make σ ₁ smaller until the calculated half-width of PL spectrum is smaller than the half-width of experimental PL spectrum, then the corresponding size separation variable is σ ₂ ; otherwise if the calculated half-width of PL spectrum < experimental PL spectrum half-width, then make _σ1 larger until the calculated PL spectrum half-width>experimental PL spectrum half-width, then the corresponding size separation variable is _σ2 ; the central size σ of quantum dots is at σ Between ₁ and σ ₂ ; Then use the dichotomy method to obtain the size separation variable σ _tone , so that the half-peak width of the PL spectrum corresponding to the σ _tone satisfies |E _{0 half} -E _half |<=0.001, σ=σ _tone ; §E. At this time, the size distribution of quantum dots is:

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