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Stock-based Compensation Expense (Tables)
3 Months Ended
Mar. 31, 2023
Stock-based Compensation Expense [Abstract]  
Weighted-Average Assumptions for Stock Options

Employee Stock Options:
 
Three Months Ended
March 31,
 
   
2023
   
2022
 
Risk-free interest rate
   
3.6
%
   
1.7
%
Dividend yield
   
0.0
%
   
0.0
%
Volatility
   
47.5
%
   
55.2
%
Expected life*
 
6.3 years
   
6.3 years
 

*
In 2021, our Compensation Committee approved an amendment to the 2011 Equity Incentive Plan, or 2011 Plan, and the 2020 Equity Incentive Plan, or 2020 Plan, that increased the contractual term of stock options granted under these plans from seven years to ten years for stock options granted on January 1, 2022 and thereafter. We determined that we are unable to rely on our historical exercise data as a basis for estimating the expected life of stock options granted to employees following this change because the contractual term changed and we have no other means to reasonably estimate future exercise behavior. We therefore used the simplified method for determining the expected life of stock options granted to employees in the three months ended March 31, 2023 and 2022. Under the simplified method, we calculate the expected term as the average of the time-to-vesting and the contractual life of the options. As we gain additional historical information, we will transition to calculating our expected term based on our historical exercise patterns. 
Weighted-Average Assumptions for ESPP

ESPP:
 
Three Months Ended
March 31,
 
   
2023
   
2022
 
Risk-free interest rate
   
5.2
%
   
0.6
%
Dividend yield
   
0.0
%
   
0.0
%
Volatility
   
36.7
%
   
50.2
%
Expected life
 
6 months
   
6 months
 
Stock-Based Compensation Expense

The following table summarizes stock-based compensation expense for the three months ended March 31, 2023 and 2022 (in thousands):


 
Three Months Ended
March 31,
 
   
2023
   
2022
 
Cost of sales
 
$
119
   
$
160
 
Research, development and patent expense
   
19,567
     
19,082
 
Selling, general and administrative expense
   
7,262
     
6,994
 
Total
 
$
26,948
   
$
26,236