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Stock-based Compensation Expense (Tables)
6 Months Ended
Jun. 30, 2023
Stock-based Compensation Expense [Abstract]  
Weighted-Average Assumptions for Stock Options

Employee Stock Options:
 
Six Months Ended
June 30,
 
   
2023
   
2022
 
Risk-free interest rate
   
3.6
%
   
1.8
%
Dividend yield
   
0.0
%
   
0.0
%
Volatility
   
47.3
%
   
55.1
%
Expected life
 
6.3 years
   
6.3 years
 
Weighted-Average Assumptions for ESPP

ESPP:
 
Six Months Ended
June 30,
 
   
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 and six months ended June 30, 2023 and 2022 (in thousands):

 
Three Months Ended
June 30,
   
Six Months Ended
June 30,
 
 
2023
   
2022
   
2023
   
2022
 
Cost of sales
 
$
118
   
$
53
   
$
237
   
$
213
 
Research, development and patent expense
   
19,249
     
18,500
     
38,816
     
37,582
 
Selling, general and administrative expense
   
7,194
     
5,949
     
14,457
     
12,943
 
Total stock-based compensation expense
 
$
26,561
   
$
24,502
   
$
53,510
   
$
50,738