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Income Taxes - Additional Information (Details) - USD ($) | 3 Months Ended | 12 Months Ended |  |  |
--- | --- | --- | --- | --- | ---
Sep. 30, 2016 | Sep. 30, 2020 | Sep. 30, 2019 | Sep. 30, 2018 | Dec. 29, 2018 | Oct. 01, 2017 | Sep. 30, 2017
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Foreign rate differences |  | $ (22,074,000) | $ (26,952,000) | $ (38,743,000) |  |  |
Foreign tax on U.S. provision |  | $ 4,523,000 | $ 6,547,000 | $ 2,736,000 |  |  |
Federal statutory income tax rate |  | 21.00% | 21.00% | 25.00% |  |  |
Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Percent |  |  |  | 24.50% |  |  |
Income taxes payable |  | $ 15,400,000 | $ 23,400,000 |  |  |  |
Provision (benefit) from deferred income taxes |  | (24,641,000) | 1,708,000 | $ (56,556,000) |  |  |
Accrued income taxes |  | 7,000,000.0 | 17,400,000 |  |  |  |
Prepaid income taxes |  | 17,300,000 | 5,300,000 |  |  |  |
Income tax payments |  | 52,600,000 | 38,900,000 | 22,600,000 |  |  |
Total stockholders’ equity |  | 1,438,248,000 | 1,201,998,000 | 874,589,000 |  |  | $ 885,436,000
Deferred tax assets |  | 190,963,000 | 198,634,000 |  |  |  |
Foreign tax credits |  | 8,074,000 | 0 |  |  |  |
Gross deferred amortization carryforward |  | 907,400,000 |  |  |  |  |
Valuation allowance |  | 205,423,000 | 177,663,000 | 141,950,000 |  |  | 279,683,000
Interest Expense |  | 76,428,000 | 43,047,000 | 41,673,000 |  |  |
Penalty expense |  | 0 | 0 | 0 |  |  |
Interest expense related to income tax accruals |  | 600,000 | 500,000 |  |  |  |
Accrued tax penalties |  | 0 | 0 | 0 |  |  |
Income tax provision upon recognition of unrecognized tax benefit |  | 16,100,000 |  |  |  |  |
Unrecognized tax benefits, increase in valuation allowance upon recognition |  | 7,700,000 |  |  |  |  |
Potential decrease in unrecognized tax benefits |  | 1,000,000 |  |  |  |  |
Stock-based compensation |  | 115,149,000 | 86,400,000 | 82,939,000 |  |  |
Tax benefit recognition related to stock based compensation |  | 13,400,000 | 16,600,000 | 28,300,000 |  |  |
Provision (benefit) for income taxes |  | 4,011,000 | 47,760,000 | (23,331,000) |  |  |
Income Tax Expense |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Interest Expense |  | 300,000 | 100,000 | 600,000 |  |  |
Accumulated Deficit |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Total stockholders’ equity |  | (62,267,000) | (191,390,000) | (599,409,000) |  |  | $ (650,840,000)
Accounting Standards Update 2016-16 |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Deferred tax assets |  |  |  |  | $ 75,300,000 |  |
Other Tax Assets |  |  |  |  | 6,000,000.0 |  |
Other Tax Liabilities |  |  |  |  | 3,000,000.0 |  |
Accounting Standards Update 2016-16 | Accumulated Deficit |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Total stockholders’ equity |  |  |  |  | $ 72,300,000 |  |
Accounting Standards Update 2016-09 |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Windfall tax deductions not yet recognized |  |  |  |  |  | $ 37,000,000.0 |
Windfall tax deductions not yet recognized offset valuation allowance |  |  |  |  |  | $ 36,900,000 |
Other Current Liabilities |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Accrued income taxes |  | 1,000,000.0 | 400,000 |  |  |  |
Other Liabilities [Member] |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Accrued income taxes |  | 7,400,000 | 5,600,000 |  |  |  |
Net Decrease in Deferred Tax Liability |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Provision (benefit) from deferred income taxes |  |  |  | 14,100,000 |  |  |
Patents |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Foreign tax on U.S. provision |  |  |  | 2,700,000 |  |  |
Realignment |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Foreign rate differences |  |  |  | 24,000,000 |  |  |
State - Massachusetts |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Income taxes payable |  |  |  | 1,700,000 |  |  |
State - Massachusetts | Research Tax Credit Carryforward |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Credit carryforwards |  | 26,900,000 |  |  |  |  |
Domestic Country |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Net operating loss carryforwards |  | 128,700,000 |  |  |  |  |
Valuation allowance |  | 171,300,000 |  |  |  |  |
Domestic Country | Expire in 2030 to 2040 |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Credit carryforwards |  | 42,200,000 |  |  |  |  |
Domestic Country | Expire in 2021 to 2037 |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Net operating loss carryforwards |  | 53,200,000 |  |  |  |  |
Domestic Country | Not Expire |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Net operating loss carryforwards |  | 75,500,000 |  |  |  |  |
Foreign Country |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Net operating loss carryforwards |  | 58,400,000 |  |  |  |  |
Credit carryforwards |  | $ 8,100,000 |  |  |  |  |
Credit carryforwards expiration |  | 2030 |  |  |  |  |
Foreign tax credits |  | $ 4,400,000 |  |  |  |  |
Valuation allowance |  | $ 34,100,000 |  |  |  |  |
Foreign Country | Minimum |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Non-U.S. tax credit carryforwards expiration |  | 2030 |  |  |  |  |
Foreign Country | Maximum |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Non-U.S. tax credit carryforwards expiration |  | 2035 |  |  |  |  |
KOREA, REPUBLIC OF | Paid in 2017 |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Income tax examination, estimate of possible loss | $ 12,000,000 |  |  |  |  |  |
KOREA, REPUBLIC OF | Additional Exposure |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Income tax examination, estimate of possible loss |  | $ 17,000,000 |  |  |  |  |
Windfall Tax Benefit |  |  |  |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |  |  |  |
Provision (benefit) for income taxes |  | $ 1,300,000 | $ 6,700,000 | $ 13,200,000 |  |  |

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