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CLAIMS
1. (Amended) A polymer substrate with hard coating layer comprising a polymer substrate having a thickness of 1 mm to 20 mm and a hard coating layer on the surface thereof; wherein,
the hard coating layer comprises:
a cured underlayer laminated on the surface of the polymer substrate, containing 10 to 90 parts by weight of multifunctional acrylate and 90 to 10 parts by weight of inorganic oxide fine particles and/or a hydrolysis-condensation product of an organic silicon compound, and having a thickness of 1 u.m to 20 urn, and
a silicon oxide layer that makes direct contact with the cured underlayer on the opposite side from the polymer substrate, is formed by PE-CVD using an organic silicon compound as raw material, and satisfies all of the following requirements (a) to (c):
(a) film thickness of the silicon oxide layer is within the range of 3.5 urn to 9.0
fxm,
(b) maximum indentation depth of the surface of the silicon oxide layer, as determined by measuring nanoindentation under conditions of a maximum load of 1 mN, is 150 nm or less, and
(c) the value of critical compression ratio K of the silicon oxide layer, as defined by formula (1) in a 3-point bending test of the polymer substrate with hard coating layer that imparts indentation displacement in which the surface laminated with the silicon oxide layer becomes concave, is 0.975 or less:
K = (R - D/2)/R - (0.00215 x d) Formula (1)
(wherein,
D represents the total thickness (mm) of the polymer substrate
with hard coating layer,
d represents the film thickness (um) of the silicon oxide layer, R represents the bend radius (mm) of the polymer substrate with hard coating layer, measured when the silicon oxide layer begins to separate from a cut line (separation starting line) drawn in advance at the location of the central fulcrum point where a weight is applied in a 3-point bending test).
2. The polymer substrate with hard coating layer according to claim 1,
wherein the ratio of infrared absorbance of the silicon oxide layer at a wave number of 930 cm"1 to that at a wave number of 1020 cm"1 (0,930/001020) is 0.30 or less.

3. The polymer substrate with hard coating layer according to claim 1 or 2, wherein the ratio of infrared absorbance of the silicon oxide layer at a wave number of 1280 cm-1 to that at a wave number of 1020 cm"1 (ai2so/aio2o) is within the range of 0.002 to 0.020.
4. The polymer substrate with hard coating layer according to any of claims 1 to 3, wherein indentation hardness of the surface of the silicon oxide layer as determined by measuring nano indentation under conditions of a maximum load of 1 mN is 3.0 GPa or more.
5. The polymer substrate with hard coating layer according to any of claims 1 to 4, wherein surface roughness (Ra) of the silicon oxide layer when measured using the dynamic force mode (DFM) of a scanning probe microscope under conditions of observing by 5.0 um square is 5.0 nm or less.
6. The polymer substrate with hard coating layer according to any of claims 1 to 5, containing a (meth)acrylic resin containing 0.1 to 5 mol/kg of hydroxyl groups, amino groups, carboxyl groups, alkoxysilyl groups or a combination thereof in the compound thereof.

7. A method for producing the polymer substrate with hard coating layer according to any of claims 1 to 6, comprising: forming the cured underlayer by coating a precursor material composition containing 10 to 90 parts by weight of a multi-functional acrylate and 90 to 10 parts by weight of an inorganic oxide fine particle and/or silicon compound hydrolysis-condensation product onto the polymer substrate followed by drying and heat curing or active energy ray curing.
8. The method for producing the polymer substrate with hard coating layer according to claim 7, wherein the surface of the cured underlayer is adjusted by plasma excitation or colliding an ionized inert gas with the surface of the cured underlayer.
9. The method for producing the polymer substrate with hard coating layer according to claim 7 or 8, wherein the silicon oxide layer is formed by making the average deposition rate (nm/sec) from the start of deposition to 30 seconds after

the start of deposition to be 1 nm/sec or less.
10. The method for producing the polymer substrate with hard coating layer according to claim 9, wherein the silicon oxide layer is formed by making the average deposition fate (nm/sec) starting from 30 seconds after the start of deposition to be 2 nm/sec or more.
11. The method for producing the polymer substrate with hard coating layer according to claim 10, wherein the deposition rate of the silicon oxide layer is increased continuously or incrementally in two or more steps.