Nitrogen doped silicon wafer and manufacturing method thereof

1. A method for manufacturing a nitrogen doped silicon wafer from a silicon single crystal doped with nitrogen, the method comprising the steps of:

(1) evaluating a first relationship, said first relationship being a relationship of density of oxygen precipitates (as-grown precipitates) to a heating temperature of a silicon single crystal when a nitrogen concentration of the silicon single crystal is changed under a heat treatment condition that remains constant and at a predetermine oxygen concentration, said evaluating step including a numerical calculation to obtain a radius of each of the oxygen precipitates (as-grown precipitates) that can remain in a heating experiment based on the heat treatment condition; and

(2) deriving a second relationship, said second relationship being a relationship for treating relational equations, using a variable of which at least the nitrogen concentration of the silicon single crystal and a cooling rate in a first temperature range in which the density of the oxygen precipitates (as grown precipitates) increases during crystal growth, the relationship relating the density to the radius of the oxygen precipitate (as grown precipitates), introduced in the silicon single crystal doped with nitrogen at the time of crystal growth, based on the step of evaluating a first relationship;

wherein an oxygen concentration of the silicon single crystal and density of oxygen precipitates to be obtained after a heat treatment depending on each condition of a temperature process during epitaxial growth or annealing at a temperature of 1100° C. or more are determined by calculating and predicting the density of the oxygen precipitates using the numerical calculation of the evaluating step by using the first relationship, which relates the density to the radius of the oxygen precipitates, the first relationship having been obtained in the evaluating step, and

wherein the density of the oxygen precipitates to be obtained after the heat treatment is controlled to a predetermined value by controlling the nitrogen concentration, the predetermined oxygen concentration and the temperature process of the heat treatment, and the density of the oxygen precipitates being obtained under conditions for obtaining a density of oxygen precipitates of 5×10 8 units/cm 3 after a heat treatment by using the nitrogen concentration, the predetermined oxygen concentration and each condition of the temperature process of the heat treatment.

2. The method according to claim 1 , wherein the first temperature range, in which the density of the oxygen precipitates increases during crystal growth, is from 1150° C. to 1020° C.

3. A nitrogen doped silicon wafer manufactured from a silicon single crystal doped with nitrogen, wherein

an epitaxially grown wafer or a high-temperature annealed silicon wafer is manufactured by pulling up a silicon ingot by the CZ method or MCZ method, cutting out a silicon wafer from the ingot, and pre-annealing the silicon wafer,

wherein density of oxygen precipitates appropriate for an intended application of the epitaxially grown wafer or the high-temperature annealed silicon wafer is determined using the method according to claim 1 ,

wherein, based on the oxygen and nitrogen concentration during growth of the silicon single crystal, a cooling rate at the time of pulling up the silicon ingot, a temperature and holding time of pre-annealing, and a temperature and holding time of hydrogen baking for the epitaxially grown wafer or a thermal annealing rate in a predetermined temperature range of high-temperature annealing for the high-temperature annealed silicon wafer are determined, so that the determined density of oxygen precipitates is obtained, and

wherein a wafer with a density of oxygen precipitates of 5×10 8 units/cm 3 or more is manufactured under conditions determined in the foregoing.

4. A nitrogen doped silicon wafer whose density of oxygen precipitates is controlled to 8×10 8 units/cm 3 or more based on conditions predicted by the method according to claim 1 .

5. A nitrogen doped silicon wafer whose density of oxygen precipitates is 5×10 8 units/cm 3 or more using the method according to claim 1 , wherein a cooling rate is set to 0.76° C./minute or faster in a temperature range of from 1150° C. to 1020° C. during crystal growth.

6. A nitrogen doped silicon wafer whose density oxygen precipitates is controlled to 8×10 8 units/cm 3 or more using the method according to claim 2 .

7. A nitrogen doped silicon wafer whose density oxygen precipitates is 5×10 8 units/cm 3 or more using the method according to claim 2 , wherein a cooling rate is set to 0.76° C./minute or faster in a temperature range of from 1150° C. to 1020° C. during crystal growth.

8. A method for manufacturing a silicon wafer from a silicon single crystal doped with nitrogen, the method comprising the steps of:

setting a cooling rate around 1100° C. during crystal growth, after measurement with a heat transfer analysis or a thermocouple;

setting a size distribution of an oxygen precipitate in an as-grown state in the silicon single crystal, using a nitrogen concentration in the silicon single crystal and the cooling rate, using a first equation and a second equation, wherein

the first equation is given by

BMD=6.4×10 −19 N 1.39 R −1.163 ,

where BMD is a density of the as-grown oxygen precipitates (units/cm 3 ), N is the nitrogen concentration (atoms/cm 3 ), and R is a radius of the as-grown oxygen precipitate, and

the second equation is given by

Saturation BMD density=7.5×10 8 CR 1.5 ,

where CR is the cooling rate around 1100° C. during crystal growth (° C./minute); and

setting an oxygen precipitate density using a program calculated by a third equation and a fourth equation relating at least one of growth and disappearance of the oxygen precipitate in a heat treatment process of the silicon wafer with the size distribution of the oxygen precipitate,

wherein the third equation is given by

dR/dt=DΩ(Co−Co i )/R, and

the fourth equation is given by

Co i =Co eq exp (2Ωσ/Rk β T),

where R is a radius of the oxygen precipitate, D is a diffusion coefficient of oxygen, Ω is a volume of SiO 2 per oxygen atom, Co is an oxygen concentration, Co i is an oxygen concentration at an interface of the precipitate, Co eq is a thermal equilibrium concentration of oxygen, σ is a surface energy between SiO 2 and silicon, k β is the Boltzmann constant, and T is an absolute temperature.

9. A method for manufacturing a nitrogen doped silicon wafer from a silicon single crystal doped with nitrogen, the method comprising the steps of:

evaluating a relationship of density of oxygen precipitates (as-grown precipitates) to a heating temperature of a silicon single crystal when a nitrogen concentration of the silicon single crystal is changed under a heat treatment condition that remains constant and at the predetermined oxygen concentration, said evaluating step including a numerical calculation to obtain a radius of each of the oxygen precipitates (as-grown precipitates) that can remain in a heating experiment based on the heat treatment condition; and

deriving a relationship for treating relational equations, using a variable of which at least the nitrogen concentration of the silicon single crystal and a cooling rate in a temperature range in which the density of the oxygen precipitates (as-grown precipitates) increases during crystal growth, the relationship relating the density to the radius of the oxygen precipitate (as-grown precipitates), introduced in the silicon single crystal doped with nitrogen at the time of crystal growth, based on the evaluating step;

wherein an oxygen concentration of the silicon single crystal and density of oxygen precipitates to be obtained after a heat treatment depending on each conditions of a temperature process during epitaxial growth or annealing at a temperature of 1100° C. or more are determined by calculating and predicting the density of the oxygen precipitates using the numerical calculation of the evaluating step by using the relationship relating the density to the radius of the oxygen precipitates, obtained in the evaluating step,

wherein the density of the oxygen precipitates to be obtained after the heat treatment is controlled to a predetermined value by controlling the nitrogen concentration, the predetermined oxygen concentration and the temperature process of the heat treatment, and the density of the oxygen precipitates is obtained under conditions for obtaining a density of oxygen precipitates of 5×10 8 unites/cm 3 after a heat treatment by using the nitrogen concentration, the predetermined oxygen concentration and the each conditions of the temperature process of the heat treatment,

wherein the numerical calculation in the evaluating step uses a first equation and a second equation relating at least one of growth and disappearance of the oxygen precipitate in a heat treatment process of the silicon wafer

wherein the first equation is given by

dR/dt=DΩ(Co−Co i )/R, and

the second equation is given by

Co i Co eq exp (2Ωσ/Rk β T),

where R is a radius of the oxygen precipitate, D is a diffusion coefficient of oxygen, Ω is a volume of SiO 2 per oxygen atom, Co is an oxygen concentration, Co i is an oxygen concentration at an interface of the precipitate, Co eq is a thermal equilibrium concentration of oxygen, σ is a surface energy between SiO 2 , and silicon, kis the Boltzmann constant, and T is an absolute temperature; and

wherein the relational equations in the deriving the relationship is uses a third equation and a fourth equation,

wherein the third equation given by

BMD=6.4×10 −19 N 1.39 R −1.163 ,

where BMD is a density of the as-grown oxygen precipitates (units/cm 3 ), N is the nitrogen concentration (atoms/cm 3 ), and R is a radius of the as-grown oxygen precipitate, and

wherein the fourth equation given by

Saturation BMD density=7.5×10 8 CR 1.5 ,

where CR is the cooling rate around 1100° C. during crystal growth (° C./minute).