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Income Taxes - Provision (Benefit) (Details) - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended
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Jun. 30, 2023 | Jun. 30, 2022 | Jun. 30, 2023 | Jun. 30, 2022
Income Tax Expense (Benefit), Continuing Operations [Abstract] |  |  |  |
Income tax expense (benefit) | $ (1,207) | $ 7,293 | $ (9,107) | $ (560)
Deferred tax benefit resulting from the extension of a tax incentive in China |  |  | 1,400 |
Benefit related to stock compensation windfalls |  |  |  | 4,600
Charge to increase the deferred tax liability to reflect a change in the blended state income tax rate that results from the sale of the semiconductor business assets |  |  |  | $ 700
Pre-tax income not subject to income taxes | $ 18,500 |  | $ 18,500 |

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