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Income Taxes - Provision (Benefit) (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended
--- | --- | ---
Mar. 31, 2023 | Mar. 31, 2022 | Mar. 31, 2023 | Mar. 31, 2022
Income Tax Expense (Benefit), Continuing Operations [Abstract] |  |  |  |
Income tax expense (benefit) | $ (3,260) | $ (3,173) | $ (7,900) | $ (7,853)
Deferred tax benefit resulting from the extension of a tax incentive in China |  |  | 1,400 |
Benefit related to stock compensation windfalls |  |  |  | 4,500
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 |  |  |  | 600
Pre-tax income not subject to income taxes | $ 17,100 |  | $ 17,100 |
Pre-tax gains (losses) |  | $ (1,800) |  | $ (5,000)

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