# US 8,571,812 B2 · Method for mapping oxygen concentration

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- Number: US 8,571,812 B2
- Document ID: US8571812B2
- Status: Granted
- Kind: B2
- Application number: 13/818,744
- Filed: 2011-08-30
- Published: 2013-06-20
- Granted: 2013-10-29
- Earliest claimed: 2010-09-02
- Assignees: Commissariat A L'energie Atomique Et Aux Energies Alternatives
- Applicants: Jordi Veirman; Sebastien Dubois; Nicolas Enjalbert
- Inventors: Jordi Veirman; Sebastien Dubois; Nicolas Enjalbert
- Web page: https://patentgrep.com/patent/US8571812B2

## CPC

- G01N 27/041: {of a solid body}
- G06F 17/11: for solving equations {, e.g. nonlinear equations, general mathematical optimization problems (optimization specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method for determining the oxygen concentration of a sample made of a semiconductor material includes a heat treatment step of the sample to form thermal donors, the measurement of the resistivity in an area of the sample, the determination of the thermal donor concentration from a relation expressing the charge carrier mobility according to an ionized dopant impurity concentration, by adding to the dopant impurity concentration four times the thermal donor concentration, and from the measured resistivity value. The method finally includes determining the oxygen concentration from the thermal donor concentration.

## Claims

### Claim 1

A method for determining the oxygen concentration of a sample made of a semiconductor material comprising the steps of:
a) submitting the sample to a heat treatment to form thermal donors,
b) measuring the resistivity in an area of the sample,
c) determining the thermal donor concentration from:
a relation expressing the mobility of charge carriers according to an ionized dopant impurity concentration by adding to the ionized dopant impurity concentration four times the thermal donor concentration, and
the measured resistivity value, and
d) determining the oxygen concentration of the sample from the thermal donor concentration.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the relation expressing mobility is written as:
μ
=
μ
min
⁢
T
n
β1
+
(
μ
max
-
μ
min
)
⁢
T
n
β2
1
+
(
N
A
/
D
+
4
×
N
TDD
N
ref
⁢
T
n
β3
)
α
⁢
⁢
T
n
β4
,
where:
Tn is equal to T/300, T being temperature,
NA/D is the ionized dopant impurity concentration of the sample,
NTDD is the thermal donor concentration,
α, β1, β2, β3, β4, μmax, μmin, Nref are constant parameters according to the nature of the charge carriers.

### Claim 3 (depends on 1)

The method according to claim 1, comprising, after having determined the oxygen concentration, a step of heat treatment at a temperature greater than or equal to 650° C.

### Claim 4 (depends on 1)

The method according to claim 1, wherein steps b) and c) are repeated in several areas of the sample to perform a mapping.

### Claim 5 (depends on 1)

The method according to claim 1, wherein the heat treatment has a duration such that the resistivity of the sample varies by at least 10% with respect to its initial value.

### Claim 6 (depends on 5)

The method according to claim 5, wherein the duration of the heat treatment ranges between 1 minute and 1000 minutes.

### Claim 7 (depends on 1)

The method according to claim 1, initially comprising a step of heat treatment at a temperature greater than or equal to 650° C.

### Claim 8 (depends on 7)

The method according to claim 7, comprising determining the dopant impurity concentration of the sample by a resistivity measurement.