JP5846899B2 - Semiconductor substrate analysis method - Google Patents

Description

  The present invention relates to a method for analyzing a semiconductor substrate, and more particularly to a method for analyzing a surface recombination velocity of a semiconductor substrate.

  As a method for analyzing a semiconductor substrate typified by a silicon substrate, a microwave photoconductive decay (μ-PCD) method is often used. The μ-PCD method is an analysis method using the fact that there is a correlation between the conductivity of the semiconductor substrate depending on the carrier density and the reflection intensity of the μ wave irradiated on the semiconductor substrate. Here, the time during which electrons or holes can exist as carriers, in other words, the time from when electrons or holes are generated until they are trapped at the level in the gap is called the carrier lifetime. In the μ-PCD method, the lifetime of the carrier of the semiconductor substrate can be measured from the attenuation of the reflection intensity of the μ wave using the above correlation. That is, by analyzing the semiconductor substrate using the μ-PCD method, the lifetime of the carrier of the semiconductor substrate can be measured in a non-destructive and non-contact manner (see Patent Document 1). Since the carrier lifetime is inversely proportional to the defect level density in the semiconductor substrate, the crystal state of the semiconductor substrate can be evaluated from the carrier lifetime.

  The outline of the μ-PCD method is as follows. First, the surface of a sample semiconductor substrate is irradiated with laser light to generate excess carriers of electrons and holes in the semiconductor substrate, thereby increasing the carrier density in the semiconductor substrate. When the laser irradiation is stopped, the generated excess carriers are recombined and disappear, so that the carrier density decreases. Here, when the carrier density of the semiconductor substrate increases or decreases, the conductivity of the semiconductor substrate also increases or decreases accordingly.

  At this time, from the start of the laser irradiation until the attenuation of excess carriers on the semiconductor substrate ends, the semiconductor substrate is irradiated with μ waves, and the intensity of the reflected μ waves is measured, corresponding to the change in carrier density in the above process. The intensity of the reflected μ wave to be measured also changes. That is, the lifetime of the carrier density can be measured from the attenuation of the reflected μ wave intensity.

However, the lifetime (hereinafter referred to as primary mode lifetime τ ₁ ) obtained from the measurement of the reflected μ wave intensity by the μ-PCD method is the lifetime of excess carriers in the semiconductor substrate (hereinafter referred to as bulk lifetime τ _b). Is not necessarily called). In many cases, the primary mode lifetime τ ₁ is not only the contribution of the bulk lifetime τ _b , but also a phenomenon in which excess carriers recombine and disappear on the surface of the semiconductor substrate (hereinafter, this phenomenon is called surface recombination, This phenomenon includes the contribution of the surface recombination velocity S).

Therefore, a method has been proposed in which the crystal state of the semiconductor substrate is evaluated by separating the contribution of the bulk lifetime τ _{b and} the contribution of the surface recombination velocity S from the primary mode lifetime τ ₁ (see Non-Patent Document 1). Further, the semiconductor substrate is treated with a solution in which iodine is dissolved in an organic solvent, chemical passivation is performed, and the contribution of the surface recombination velocity S in the first-order mode lifetime τ ₁ is sufficiently reduced to make the bulk crystal state of the semiconductor substrate. A method for evaluating the above has also been proposed (see Patent Document 2).

JP 59-55013 A JP-A-8-335618

Usami Akira, Shinichi Shindate, Eiji Kudo, “Separation Measurement of Lifetime and Surface Recombination Velocity of Semiconductor Wafers by Non-contact Method”, Applied Physics, Vol. 49, No. 12 (1980), p. 1192-1197

For example, in the separation evaluation method of the surface recombination velocity S and the bulk lifetime τ _b disclosed in Non-Patent Document 1, it is necessary to prepare a plurality of semiconductor substrates that are different only in thickness and have the same other conditions, There was a problem that preparation was complicated.

Also, in the method shown in Patent Document 2 in which the contribution of the surface recombination velocity S to the primary mode lifetime τ ₁ is made sufficiently small to evaluate the crystal state of the semiconductor substrate, so-called S-lowering, It is not assumed that the coupling speed S is evaluated.

  As described above, it has been impossible to simply obtain the surface recombination velocity S of the semiconductor substrate by using the μ-PCD method and thereby analyze the state of the surface of the semiconductor substrate.

  In view of such a problem, an object is to provide a method for simply analyzing the surface state of a semiconductor substrate using a μ-PCD method. In particular, an object is to provide a method of approximately obtaining the surface recombination velocity S of the semiconductor substrate using the μ-PCD method.

In the disclosed invention, by using a semiconductor substrate having a small thickness, the contribution of the surface of the semiconductor substrate in the primary mode lifetime τ ₁ measured by the μ-PCD method is made sufficiently larger than the contribution of the bulk of the semiconductor substrate. Thus, in the S-τ _b curve obtained by using the μ-PCD method and using the surface recombination velocity S and the bulk lifetime τ _b as variables, the approximate surface recombination with the bulk lifetime τ _b being infinite. The speed S can be determined. Specifically, the semiconductor substrate is analyzed using the following method.

One embodiment of the disclosed invention uses a semiconductor substrate in which the thickness W, the minority carrier diffusion constant D, and the bulk lifetime τ _b satisfy the following formula (1).

Then, using the microwave photoconductive decay method, the primary mode lifetime τ ₁ is measured from the attenuation of the reflection intensity of the microwave reflected from the surface of the semiconductor substrate, and the thickness W, minority carrier diffusion constant D, and primary mode life are measured. By substituting time τ ₁ , a curve represented by the following formula (2) using the surface recombination velocity S and bulk lifetime τ _b of the semiconductor substrate as variables is obtained.

Then, the semiconductor substrate is analyzed by obtaining an approximate surface recombination velocity S from the limit value of the surface recombination velocity S when the bulk lifetime τ _b is infinite in the curve represented by the equation (2).

In the above, it is preferable that the thickness W of the semiconductor substrate is 50 μm or more and 1.5 mm or less. Further, the bulk lifetime τ _b of the semiconductor substrate is preferably 100 μsec or more. A silicon substrate is preferably used as the semiconductor substrate.

  Further, it is preferable to perform a treatment with hydrofluoric acid as a surface treatment on the semiconductor substrate before the measurement by the microwave photoconductive decay method. Moreover, it is preferable that the surface recombination velocity S of the semiconductor substrate after the surface treatment is 100 cm / sec or more and 100000 cm / sec or less.

  The disclosed invention can provide a method for simply analyzing the surface state of a semiconductor substrate using the μ-PCD method. In particular, it is possible to provide a method of approximately obtaining the surface recombination velocity S of the semiconductor substrate using the μ-PCD method.

The schematic diagram explaining the outline | summary of micro-PCD method. FIG. 10 is a flowchart illustrating a semiconductor substrate analysis method according to one embodiment of the present invention. 6 is a graph showing a solution for calculation according to one embodiment of the present invention. 6 is an S-τ _b curve obtained in analysis of a semiconductor substrate according to one embodiment of the present invention. S-τ _b curve obtained from the computer simulation of the μ-PCD method. S-tau _b curve obtained from measurement by mu-PCD method in an embodiment of the present invention. S-tau _b curve obtained from measurement by mu-PCD method in an embodiment of the present invention.

  An example of an embodiment of the present invention will be described below with reference to the drawings. However, the present invention is not limited to the following description, and it is easily understood by those skilled in the art that modes and details can be variously changed without departing from the spirit and scope of the present invention. Therefore, the present invention should not be construed as being limited to the description of the embodiments below.

  Note that the position, size, range, and the like of each component illustrated in the drawings and the like may not represent the actual position, size, range, or the like for easy understanding. Therefore, the disclosed invention is not necessarily limited to the position, size, range, or the like disclosed in the drawings and the like.

  It should be noted that ordinal numbers such as “first” and “second” in this specification and the like are added to avoid confusion among components and are not limited numerically.

(Embodiment)
In this embodiment, a semiconductor substrate analysis method for obtaining an approximate surface recombination velocity S using the μ-PCD method will be described with reference to FIGS.

  First, the principle of measuring the carrier lifetime of a semiconductor substrate by the μ-PCD method used in the analysis method described in this embodiment will be described with reference to FIGS.

  First, as shown in FIG. 1A, a semiconductor substrate 100 is irradiated with a laser beam 102 and an irradiation μ wave 104. Irradiation with the laser light 102 generates excess carriers of electrons (black circles in FIG. 1) and holes (white circles in FIG. 1) in the semiconductor substrate 100. When excess carriers are generated and the carrier density in the semiconductor substrate 100 increases, the conductivity of the semiconductor substrate 100 also increases.

  The irradiation μ wave 104 is reflected by the surface of the semiconductor substrate 100, and the reflected μ wave 106 a is detected by the μ wave detector 108. At this time, since the reflection intensity of the reflected μ wave 106a has a substantially linear relationship with the conductivity of the semiconductor substrate 100, that is, the carrier density, the μ wave detector 108 increases the number of excess carriers generated in the semiconductor substrate 100 by laser irradiation. The intensity of the reflected μ wave 106a to be detected is increased.

  Next, as shown in FIG. 1B, the irradiation of the laser light 102 on the semiconductor substrate 100 is stopped. When the irradiation of the laser beam 102 is stopped, generation of excess carriers of electrons and holes in the semiconductor substrate 100 is also stopped. Conversely, excess carriers generated by the laser beam 102 begin to recombine at crystal defects or the like in the semiconductor substrate 100, so that the carrier density in the semiconductor substrate 100 decreases. As the carrier density decreases, the conductivity of the semiconductor substrate 100 also decreases, so that the intensity of the reflected μ wave 106b detected by the μ wave detector 108 also attenuates. Therefore, the decrease amount of the carrier density of the semiconductor substrate 100 can be obtained from the attenuation of the reflected microwave 106b to be detected, and the lifetime of the carrier can be obtained from the time required for the decrease of the carrier density.

  However, the carrier lifetime measured by using the μ-PCD method in this way is a mixture of the contribution of the surface of the semiconductor substrate 100 and the contribution of the bulk of the semiconductor substrate 100. Therefore, a method for theoretical analysis of carrier lifetime measured by the μ-PCD method will be described below.

In the following, the formulation is performed by paying attention to the lifetime of excess minority carriers injected at a low level by the laser beam 102. Here, in this embodiment, the semiconductor substrate 100 is assumed to be p-type, and minority carriers are considered to be electrons. The semiconductor substrate 100 has a thickness W, a minority carrier diffusion constant D, a bulk lifetime τ _b , and a surface recombination rate S. Here, the bulk lifetime τ _b is the lifetime of excess minority carriers in the bulk of the semiconductor substrate 100. The surface recombination speed S is a recombination speed of excess minority carriers on the surface of the semiconductor substrate 100. The surface recombination velocity S is determined by the surface irradiated with the laser light 102 of the semiconductor substrate 100 (hereinafter also referred to as the surface of the semiconductor substrate 100) and the opposite surface (hereinafter also referred to as the back surface of the semiconductor substrate 100). The same.

  Since the excess minority carrier density Δn (x, t) injected by the laser beam 102 follows a continuous equation, it is expressed as in equation (3).

  Here, the excess minority carrier density Δn (x, t) uses the distance x from the surface of the semiconductor substrate 100 and the time t as variables. The distance x from the surface of the semiconductor substrate 100 is a coordinate with the x axis perpendicular to the surface of the semiconductor substrate 100, x = 0 is the surface of the semiconductor substrate 100, and x = W is the back surface of the semiconductor substrate 100.

  The first term on the right side of Equation (3) means the diffusion current, and the second term means recombination. In the continuous equation, there is usually a term representing the contribution of drift, but as described above, the contribution of diffusion is dominant in the excess minority carriers injected at a low level, and the contribution of drift can be ignored. Thereby, Formula (3) becomes linear. From the form of Equation (3), Δn (x, t) can be separated into variables, and can be expressed as Equation (4) using the time portion F (t) and the space portion φ (x).

  Substituting equation (4) into equation (3) yields equation (5).

Here, the constant const appearing in the equation (5) is expressed as −K ² D for convenience.

  The time portion F (t) and space portion φ (x) general solutions of Equation (5) are as shown in Equation (6) and Equation (7), respectively.

  Here, τ in the equation (6) corresponds to the lifetime of the excess minority carrier measured by the μ-PCD method, and is represented by the following equation (8).

  Further, since the surface recombination velocity is S on the front surface (x = 0) of the semiconductor substrate 100 and the back surface (x = W) of the semiconductor substrate 100, assuming this as a boundary condition, the following equations (9) and (9) (10) is derived.

  By imposing the boundary condition represented by equation (9) on equation (7), equation (11) is derived, and α can be represented by K.

Here S _M in formula (11) is obtained by dividing the surface recombination velocity S is the minority carrier diffusion constant D. Furthermore, Formula (12) is derived by imposing the boundary condition represented by Formula (10) on Formula (7).

  Here, Expression (12) is a characteristic equation of Expression (6) and Expression (7), and K in Expression (12) is its eigenvalue. Thus, K has an infinite number of solutions. Here, FIG. 3 shows a graph in which the vertical axis represents the left side and the right side of Equation (12), and the horizontal axis represents KW / π [rad / π]. In FIG. 3, the solid line represents the left side of Expression (12), and the dotted line represents the right side of Expression (12). The value of K corresponding to the intersection of the practice and the dotted line is the eigenvalue of Expression (12).

In this way, K has an infinite number of discrete solutions, and K → K _i (i = 1, 2, 3,...) And subscripts in order from the smallest value of K, From equation (8), the lifetime τ of the excess minority carrier also has a discrete infinite number of solutions such as τ → τ _i (i = 1, 2, 3,...). In particular, τ _{1 of} τ _i has the longest lifetime and is referred to as a primary mode lifetime τ ₁ . Further, by setting K → K _i and τ → τ _i , F (t) → F _i (t) (i = 1, 2, 3,...), Φ from Expression (6) and Expression (7) A natural mode of (x) → φ _i (x) (i = 1, 2, 3,...) Is given.

An arbitrary excess minority carrier density Δn (x, t) can be expanded by a linear combination of these eigenmodes, and by integrating this over x in the range of the thickness W of the semiconductor substrate 100, the excess minority carrier density An attenuation curve is obtained. When the attenuation curve of the excess minority carrier density is sufficiently developed, only the first-order eigenmode component remains. Therefore, the excess minority carrier lifetime τ can be regarded as the primary mode lifetime τ ₁ . Thereby, the lifetime of the carrier measured by the μ-PCD method can also be regarded as the primary mode lifetime τ ₁ . Therefore, in this specification, the carrier lifetime measured by the μ-PCD method is referred to as a primary mode lifetime τ ₁ .

Here, Equation (13) obtained using the primary mode lifetime τ ₁ in Equation (8) and Equation (14) obtained using K ₁ in Equation (12) are shown below.

From the equation (13), the primary mode lifetime τ ₁ measured by the μ-PCD method is the contribution of the bulk of the semiconductor substrate 100 (contribution of the bulk lifetime τ _b ) to the first term on the right side of the equation (13), It can be seen that the second term on the right side of Equation (13) has a contribution from the surface of the semiconductor substrate 100 (contribution of the surface recombination velocity S).

Further, when K ₁ is eliminated from the equations (13) and (14), the surface recombination velocity S is expressed by the equation (15) expressed by the thickness W of the semiconductor substrate 100, the first-order mode lifetime τ ₁ , and the bulk lifetime τ _b. ) Is obtained.

By substituting the primary mode lifetime τ ₁ measured by the μ-PCD method into the equation (15), the surface recombination velocity S can be expressed by the bulk lifetime τ _b and a known constant. That is, an S-τ _b curve is obtained with the surface recombination velocity S on the vertical axis and the bulk lifetime τ _b on the horizontal axis.

In the non-patent document 1 described above, two semiconductor substrates having different thicknesses are used, and the primary mode lifetime τ ₁ is measured in each of them, and the simultaneous simultaneous equations of Equation (15) are solved to obtain the surface The recombination velocity S and the bulk lifetime τ _b are obtained. However, the surface recombination velocity S and the bulk lifetime τ _b separation evaluation method have a problem that preparation is complicated because it is necessary to prepare a plurality of semiconductor substrates that are different only in thickness and under other conditions. .

In Patent Document 2, chemical passivation treatment is performed on a semiconductor substrate to reduce the surface recombination velocity S, and the surface contribution in Equation (13) is sufficiently reduced to τ ₁ ≈τ _b . The primary mode lifetime τ ₁ measured by the μ-PCD method is approximated to the carrier lifetime of the semiconductor substrate. In such a method called S-lowering, the surface recombination velocity S cannot be evaluated in principle.

  As described above, it is difficult to easily obtain the surface recombination velocity S of the semiconductor substrate by using the μ-PCD method and thereby analyze the crystal state of the semiconductor substrate.

In view of such a problem, in the present embodiment, the contribution of the surface (contribution of the surface recombination velocity S) in the primary mode lifetime τ ₁ shown in Expression (13) is changed to the contribution of the bulk (bulk lifetime τ _b ). The approximate surface recombination velocity S is easily obtained by making it sufficiently larger than the contribution). That is, an approximate surface recombination velocity S is easily obtained in a semiconductor substrate that satisfies the equation (16).

In Equation (13) and Equation (16), since the bulk contribution exists in the term τ _b ⁻¹ , the primary mode lifetime is obtained by using a semiconductor substrate having a sufficiently long bulk lifetime τ _b. The bulk contribution in τ ₁ can be reduced.

Here, FIG. 4 shows an S-τ _b curve 110 when the surface contribution in the primary mode lifetime τ ₁ is sufficiently larger than the bulk contribution in the equation (15). In the graph shown in FIG. 4, the vertical axis represents the surface recombination velocity S, and the horizontal axis represents the bulk lifetime τ _b . In the formula (15), the bulk lifetime tau _b is present in the section of tau _b ^-1, if bulk lifetime tau _b is sufficiently large, the term tau _b ^-1 converges to 0. Therefore, in the S-τ _b curve 110 shown in FIG. 4, the surface recombination velocity S is saturated when the bulk lifetime τ _b becomes sufficiently large. The dotted line in FIG. 4 corresponds to the value of the saturated surface recombination velocity S in the S-τ _b curve 110.

In the equation (15) represented by such an S-τ _b curve, an approximate surface recombination velocity S can be obtained from the limit value of the surface recombination velocity S at the bulk lifetime τ _b → ∞.

  Hereinafter, a semiconductor substrate analysis method for obtaining an approximate surface recombination velocity S using the μ-PCD method will be specifically described with reference to the flowchart shown in FIG. The flow diagram of FIG. 2 shows a method for obtaining an approximate surface recombination velocity S using the μ-PCD method divided into five stages of Step 1 to Step 5.

The method for analyzing a semiconductor substrate described in this embodiment includes preparation of a semiconductor substrate (step 1), surface treatment of the semiconductor substrate (step 2), and measurement of the primary mode lifetime τ ₁ of the semiconductor substrate by the μ-PCD method (step 3) Derivation of S-τ _b curve using surface recombination velocity S and bulk lifetime τ _b as variables (step 4), surface recombination velocity S of bulk lifetime τ _b → ∞ in S-τ _b curve The limit value is calculated as an approximate surface recombination velocity S (step 5), and is performed in five stages.

  First, step 1: preparation of a semiconductor substrate in the flowchart of FIG. 2 will be described.

A semiconductor substrate used in the analysis method described in this embodiment has a thickness W, a minority carrier diffusion constant D, and a bulk lifetime τ _b . In the above formulation, the semiconductor substrate 100 is a p-type, but the semiconductor substrate used in this embodiment is not limited to this, and an n-type may be used.

As shown in the equation (16), the semiconductor substrate desirably has a sufficiently small bulk contribution of the semiconductor substrate and a sufficiently large contribution of the surface of the semiconductor substrate in the first-order mode lifetime τ ₁ . Therefore, K ₁ is removed from the equation (16), and this condition is expressed by the thickness W, the minority carrier diffusion constant D, and the bulk lifetime τ _b as parameters of the semiconductor substrate. Here, in Expression (13), Expression (17) in which the numerator of the second term on the right side and the denominator are multiplied by W ² is shown.

Here, referring to FIG. 3, since the left side of the equation (12) is asymptotic with KW / π = 0 and KW / π = 1, 0 <K ₁ <πW ⁻¹ . Therefore, K ₁ W in Expression (17) is 0 <K ₁ W <π. Therefore, the range of K ₁ W in formula (17) is limited. Thus, it can be said that the semiconductor substrate used in the analysis method described in this embodiment only needs to satisfy at least the following expression (18).

  Note that the semiconductor substrate used in the analysis method described in this embodiment preferably satisfies the following equation (19), and more preferably satisfies the following equation (20).

The semiconductor substrate having such a condition may have a thickness W of at least 1.5 mm, for example, preferably 10 μm or more and 1.5 mm or less, and preferably 100 μm or more and 800 μm or less. More preferred. In particular, as shown in the second term on the right side of Equation (17), the contribution of the surface of the semiconductor substrate to the primary mode lifetime τ ₁ increases in inverse proportion to the thickness W of the semiconductor substrate. Therefore, it is preferable to use a semiconductor substrate that is as thin as possible.

  Further, the bulk lifetime of the semiconductor substrate having such conditions is at least 100 μsec or more, for example, 500 μsec or more, and more preferably 10,000 μsec or more.

  The semiconductor substrate that can be used for the analysis method described in this embodiment is preferably a silicon substrate, but is not limited thereto, and a semiconductor substrate formed of germanium, silicon germanium, silicon carbide, gallium arsenide, or the like is used. You can also.

By using such a semiconductor substrate, the bulk contribution of the semiconductor substrate can be made sufficiently small and the contribution of the surface of the semiconductor substrate can be made sufficiently large in the primary mode lifetime τ ₁ . By using this, the surface recombination velocity S of the semiconductor substrate can be obtained approximately.

  Next, step 2 in the flowchart of FIG. 2 will be described.

  The semiconductor substrate used for the analysis method described in this embodiment is preferably subjected to surface treatment to increase the surface recombination speed S, and may be at least 100 cm / sec. For example, the surface recombination speed S is preferably set to 100 cm / sec or more and 100,000 cm / sec or less.

  In addition, the surface treatment of the semiconductor substrate is performed not only on the surface irradiated with the laser beam and the μ wave in the measurement by the μ-PCD method in step 3, but also on the opposite surface, and surface recombination of both surfaces is performed. It is preferable to keep the speed S substantially equal.

  As such a surface treatment, treatment with hydrofluoric acid is preferably performed. The concentration of hydrofluoric acid is, for example, preferably 0.1% by weight to 10% by weight, and more preferably 0.5% by weight to 6% by weight.

By performing such surface treatment, the contribution of the surface of the semiconductor substrate can be made sufficiently large in the first-order mode lifetime τ ₁ , and therefore the surface recombination velocity S of the semiconductor substrate can be obtained using the μ-PCD method. Can be obtained approximately.

  However, the surface treatment of the semiconductor substrate is not necessarily required. For example, the surface recombination speed S can be set to 100 cm / sec or more and 100,000 cm / sec or less by forming a natural oxide film on the silicon substrate.

Next, step 3: measurement of the primary mode lifetime τ ₁ of the semiconductor substrate by the μ-PCD method in the flowchart of FIG. 2 will be described.

In the primary mode lifetime τ ₁ , the measurement by the μ-PCD method shown in FIG. 1 is performed on a semiconductor substrate having a sufficiently small bulk contribution and a sufficiently large surface contribution. At this time, the wavelength and intensity of the laser light and μ wave applied to the semiconductor substrate may be set as appropriate in accordance with the semiconductor substrate as a sample. However, when reducing the film thickness of the semiconductor substrate as described above, it is preferable to shorten the wavelength of the laser beam because the laser beam is not absorbed by the semiconductor substrate if the wavelength of the laser beam is long. The wavelength can be 904 nm.

The measurement of the primary mode lifetime τ ₁ of the semiconductor substrate by the μ-PCD method may be performed at least at one point on the surface of the semiconductor substrate, but more preferably at a plurality of locations on the surface of the semiconductor substrate. When the primary mode lifetime τ ₁ is measured at a plurality of locations on the surface of the semiconductor substrate, the measured value at each location may be used as the primary mode lifetime τ ₁ , and the average value of the plurality of measurement locations is the primary mode lifetime. It is good also as (tau) ₁ .

Next, step 4: derivation of the S-τ _b curve using the surface recombination velocity S and the bulk lifetime τ _b as variables will be described in the flowchart of FIG.

The known thickness W of the semiconductor substrate, the minority carrier diffusion constant D, and the primary mode lifetime τ ₁ measured in step 3 are substituted into the above equation (15). Thus, the equation (15) becomes an equation with the surface recombination velocity S and the bulk lifetime τ _b as variables, and an S-τ _b curve as shown in FIG. 4 can be derived.

Finally, step 5 of the flow chart of FIG. 2: Calculation of the limit value of the surface recombination rate S of the bulk lifetime τ _b → ∞ on the S−τ _b curve as an approximate surface recombination rate S will be described.

In the S-τ _b curve obtained in step 4, all combinations of the surface recombination velocity S and the bulk lifetime τ _b are drawn, and this alone indicates which of the surface recombination velocity S and the bulk lifetime τ _b of the semiconductor substrate. You can't limit the value. However, in the method for analyzing a semiconductor substrate described in this embodiment, the contribution of the surface of the semiconductor substrate in the primary mode lifetime τ ₁ is made sufficiently larger than the contribution of the bulk through step 1 and step 2. Therefore, in Formula (13) and Formula (15), it can be considered that it converges to τ _b ⁻¹ → 0. Thereby, the surface recombination velocity S of the semiconductor substrate used in the present embodiment can be approximately obtained from the limit value of the surface recombination velocity S when the bulk lifetime τ _b is ∞ in the equation (15). . In other words, it can be regarded as the value of the saturated surface recombination velocity S of the S-tau _b curve obtained in step 4 with approximate surface recombination velocity S.

  As shown in Step 1 and Step 2, in the method for analyzing a semiconductor substrate described in this embodiment, it is necessary to prepare a plurality of semiconductor substrates that differ only in thickness and have the same other conditions as in Non-Patent Document 1. No, preparation for measurement by the μ-PCD method is simple. Therefore, by using the semiconductor substrate analysis method described in this embodiment, an approximate surface recombination velocity S of the semiconductor substrate can be easily obtained using the μ-PCD method. Thereby, the state of the surface of the semiconductor substrate can be easily analyzed using the μ-PCD method.

Here, various parameters are set for models of a plurality of semiconductor substrates having different thicknesses W, the primary mode lifetime τ ₁ is calculated by computer simulation, and an approximate surface recombination velocity S is obtained from Equation (15). The results will be described.

In this calculation, a model of a semiconductor substrate having a thickness W of 350 μm, 700 μm, and 3000 μm was used. The model of each semiconductor substrate used in this calculation assumes a p-type semiconductor substrate in which minority carriers are electrons, and parameters other than the thickness W of each model are minority carrier diffusion constants D = 30 cm ² / sec, The surface recombination speed S was set to 1000 cm / sec, and the bulk lifetime τ _{b was set to} 1000 μsec.

From these parameters, the primary eigenmode of each semiconductor substrate model was obtained, and the primary mode lifetime τ ₁ was calculated. For each model, the setting parameters minority carrier diffusion constant D, thickness W, and calculated first-order mode lifetime τ ₁ are substituted into equation (15) to derive an S-τ _b curve, and the surface at τ _b → ∞ The limit value of the recombination velocity S was determined.

The S-tau _b curves obtained from the semiconductor substrate model shown in FIG. 5 (A). Here, in FIG. 5A, the vertical axis indicates the surface recombination velocity S [cm / sec], and the horizontal axis indicates the bulk lifetime τ _b [μsec], and the S−τ _b curve 120 shows W = 350 μm. The S-τ _b curve 122 corresponds to the W = 700 μm model, and the S-τ _b curve 124 corresponds to the W = 3000 μm model. Table 1 shows the primary mode lifetime τ ₁ [μsec] of each semiconductor substrate model and the approximate surface recombination velocity S [cm / sec] at τ _b → ∞.

FIG. 5A shows that the S-τ _b curve 120 with W = 350 μm and the S-τ _b curve 122 with W = 700 μm converge when the bulk lifetime τ _b is about 1000 μsec or more. The value of the approximate surface recombination velocity S in Table 1 is also very close to the set parameter S = 1000 cm / sec. On the other hand, in the S-τ _b curve 124 of W = 3000 μm, the surface recombination velocity S diverges with respect to the bulk lifetime τ _b , and an approximate value cannot be obtained.

Thus, in the model in which the thickness W of the semiconductor substrate is thinned so that the contribution of the surface is sufficiently larger than the contribution of the bulk in the first-order mode lifetime τ ₁ , the limit value of the surface recombination velocity S in Expression (15) Thus, an approximate surface recombination velocity S can be obtained with high accuracy. On the other hand, an approximate surface recombination velocity S cannot be obtained from Equation (15) in a model in which the surface contribution is not sufficiently larger than the bulk contribution and the thickness W of the semiconductor substrate is thick.

Further, after obtaining the approximate surface recombination velocity S of the semiconductor substrate in step 5, it is also confirmed whether the surface recombination velocity S of the semiconductor substrate is surely present on the saturated region of the S-τ _b curve. it can. This is to prepare a semiconductor substrate having the same bulk lifetime τ _b as that of the semiconductor substrate from which the approximate surface recombination velocity S is obtained, and having a bulk contribution sufficiently larger than the surface contribution in the first-order mode lifetime τ ₁ . it can be performed by determining the S-tau _b curve similarly to the semiconductor substrate by.

  As a semiconductor substrate for such confirmation, a semiconductor substrate thicker than the thickness W is cut out from the same ingot from which the semiconductor substrate for which the approximate surface recombination velocity S has been obtained is cut out, and the semiconductor substrate is cut into the semiconductor substrate. It can be obtained by performing a treatment that reduces the surface recombination velocity S such as chemical passivation.

Here, the surface recombination velocity S of the model of W = 350 μm and W = 700 μm obtained by the computer simulation shown in FIG. 5A is saturated in the S-τ _b curve 120 and the S-τ _b curve 122. Check if it exists on the area. As a model of the semiconductor substrate for confirmation, a model with a thickness W = 3000 μm, a surface recombination speed S = 100 cm / sec, and the other parameters being the same was used.

FIG. 5B shows an S-τ _b curve 126 of a semiconductor substrate model for confirmation, together with the S-τ _b curve 120 and the S-τ _b curve 122. 5 from (B), the S-tau range of bulk lifetime tau _b can take the _b curve 126, S-tau _b curves 120 and S-tau _b curve 122 is seen to saturated. Here, the bulk lifetime tau _b of the semiconductor substrate models for confirmation is the same as W = 350 .mu.m models, W = 700 .mu.m bulk lifetime tau _b model. Therefore, it was shown that the surface recombination velocity S of the model with W = 350 μm and W = 700 μm surely exists on the saturated region of the S-τ _b curve 120 and the S-τ _b curve 122.

  As described above, by using the method for analyzing a semiconductor substrate described in this embodiment, the surface recombination velocity S of the semiconductor substrate can be approximately obtained using the μ-PCD method. Thereby, the state of the surface of the semiconductor substrate can be easily analyzed using the μ-PCD method.

  In this example, the results of actual analysis of a semiconductor substrate using the semiconductor substrate analysis method for obtaining an approximate surface recombination velocity S using the μ-PCD method shown in the previous embodiment are shown. 6 and FIG.

  In this example, a p-type single crystal silicon substrate was used as a sample, and Samples A to F having thicknesses of 100 μm, 150 μm, 300 μm, 700 μm, 2000 μm, and 3000 μm were used. These samples A to F were treated with 5% by weight of hydrofluoric acid as a surface treatment.

The first mode lifetime τ ₁ was measured by performing μ-PCD measurement on samples A to F. The μ-PCD measurement was performed by using a WT-2000 manufactured by Nippon Semilab Co., Ltd. and irradiating a laser with a wavelength of 904 nm and a 10 GHz μ wave.

The first-order mode lifetime τ ₁ obtained by μ-PCD measurement is substituted into Equation (15) shown in the previous embodiment to derive S-τ _b curves of Sample A to Sample F. To do. The S-tau _b curve of Sample A to Sample F shown in FIG. In FIG. 6, the vertical axis represents the surface recombination velocity S [cm / sec], and the horizontal axis represents the bulk lifetime τ _b [μsec]. Table 2 shows the approximate surface recombination velocity S [cm / sec] at the substrate thickness W, first-order mode lifetime τ ₁ [μsec], and τ _b → ∞ of each sample. The minority carrier diffusion constant D was 30 cm ² / sec assuming electrons.

From FIG. 6, it can be seen that the S-τ _b curves of Sample A to Sample D converge when the bulk lifetime τ _b is at least about 1000 μsec or more. The values of the approximate surface recombination velocity S in Table 2 are also about 3000 cm / sec for Sample A and Sample D, and about 1500 cm / sec for Sample B and Sample D. The approximate value of the surface recombination velocity S is the same digit, which can be said to be a relatively good approximation.

For sample A to sample D, the S-τ _b curves of sample E and sample F require the surface recombination velocity S to diverge with respect to the bulk lifetime τ _b , and obtain an approximate value. I can't.

As described above, by making the thickness of the semiconductor substrate preferably 50 μm or more and 1.5 mm or less, more preferably 100 μm or more and 800 μm or less, the surface contribution to the primary mode lifetime τ ₁ is sufficiently larger than the bulk contribution. Thus, it is estimated that an approximate surface recombination velocity S can be obtained from the limit value of the surface recombination velocity S at τ _b → ∞.

Further, unlike the samples A to F, the surface recombination velocity S was obtained by using the μ-PCD method for the sample in which the surface treatment was not performed and the natural oxide film was formed. Using samples G to J having substrate thicknesses of 150 μm, 300 μm, 2000 μm, and 3000 μm, μ-PCD measurement was performed in the same manner as samples A to F, and an S-τ _b curve was derived.

FIG. 7 shows S-τ _b curves of Sample G to Sample J. Here, in FIG. 7, the vertical axis represents the surface recombination velocity S [cm / sec], and the horizontal axis represents the bulk lifetime τ _b [μsec]. Table 3 shows the approximate surface recombination velocity S [cm / sec] at the substrate thickness W, first-order mode lifetime τ ₁ [μsec], and τ _b → ∞ of each sample.

From FIG. 7, it can be seen that the S-τ _b curves of Sample G and Sample H converge when the bulk lifetime τ _b is at least about 1000 μsec. The approximate surface recombination rate S values in Table 3 are also about 32000 cm / sec for sample G and about 16000 cm / sec for sample H, and approximate values for surface recombination rate S for both samples. Are the same digits and can be said to be a relatively good approximation.

For sample G and sample H, the S-τ _b curves of sample I and sample J are such that the surface recombination velocity S is diverging with respect to the bulk lifetime τ _b , and an approximate value is obtained. I can't.

As described above, even when the surface treatment is not performed with hydrofluoric acid and a natural oxide film is formed on the surface of the semiconductor substrate, the contribution of the surface to the primary mode lifetime τ ₁ is sufficiently greater than the contribution of the bulk. It was shown that the approximate surface recombination velocity S can be obtained from the limit value of the surface recombination velocity S at τ _b → ∞.

1 Step 2 Step 3 Step 4 Step 5 Step 100 Semiconductor substrate 102 Laser light 104 Irradiated μ wave 106a Reflected μ wave 106b Reflected μ wave 108 μ wave detector 110 S-τ _b curve 120 S-τ _b curve 122 S-τ _b Curve 124 S-τ _b curve 126 S-τ _b curve

Claims (5)

Using a semiconductor substrate in which the thickness W, the minority carrier diffusion constant D, and the bulk lifetime τ _b satisfy the following formula (19) ,

Using the microwave photoconductive decay method, the first-order mode lifetime τ ₁ is measured from the attenuation of the reflected intensity of the microwave reflected from the surface of the semiconductor substrate,
Substituting the thickness W, the minority carrier diffusion constant D, and the first-order mode lifetime τ ₁ , the following equation (2) using the surface recombination velocity S of the semiconductor substrate and the bulk lifetime τ _b as variables: Find the curve indicated by

In the curve shown by said Formula (2), the analysis method of the semiconductor substrate which calculates | requires the approximate surface recombination velocity S from the limit value of the said surface recombination velocity S when the said bulk lifetime (tau) _b is infinite.   The semiconductor substrate analysis method according to claim 1, wherein a thickness W of the semiconductor substrate is 50 μm or more and 1.5 mm or less. The method for analyzing a semiconductor substrate according to claim 1, wherein a bulk lifetime τ _b of the semiconductor substrate is 100 μsec or more.   The semiconductor substrate analysis method according to claim 1, wherein a silicon substrate is used as the semiconductor substrate.   The semiconductor substrate analysis method according to claim 4, wherein the semiconductor substrate is treated with hydrofluoric acid as a surface treatment before the measurement by the microwave photoconductive decay method.