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