硅基擂台：3nm之后，半导体晶圆如何突破物理极限？

import math

def calculate_die_per_wafer(wafer_diameter_mm, die_width_mm, die_height_mm):
    """
    估算单片晶圆理论可切割的芯片数量（Die Per Wafer, DPW）
    考虑了边缘无效区域的工程近似值
    """
    wafer_radius = wafer_diameter_mm / 2.0
    die_area = die_width_mm * die_height_mm
    
    # 核心算法：(π * R^2) / 芯片面积 - (π * R) / (sqrt(2 * 芯片面积))
    # 减去项是为了修正边缘无法完美拼接的损失
    term1 = math.pi * (wafer_radius ** 2) / die_area
    term2 = (math.pi * wafer_radius) / math.sqrt(2 * die_area)
    theoretical_dies = int(term1 - term2)
    
    return max(0, theoretical_dies)

# 实战场景：苹果A19 Pro芯片（假设核心面积约为 120mm²，基于台积电N3P工艺）
wafer_size = 300  # mm
chip_width = 10.95  # mm (约120平方毫米，取约11x11)
chip_height = 10.95 

die_count = calculate_die_per_wafer(wafer_size, chip_width, chip_height)
print(f"📏 单片12英寸晶圆理论芯片数量：{die_count} 颗")

# 考虑生产良率（Defect Density Yield Model - 泊松分布）
def calculate_yield(defect_density_per_cm2, die_area_cm2, alpha=4.0):
    """
    计算晶圆良率：缺陷密度越低、芯片面积越小，良率越高
    采用负二项式分布模型（更符合实际）
    """
    return (1 + (defect_density_per_cm2 * die_area_cm2) / alpha) ** (-alpha)

# 假设当前先进工艺缺陷密度为 0.03 个/cm² (世界顶尖水平)
defect_density = 0.03  
die_area_cm2 = 1.2   # 120mm² = 1.2cm²
yield_rate = calculate_yield(defect_density, die_area_cm2)

print(f"✅ 预估良率：{yield_rate * 100:.2f}%")
print(f"🎯 实际有效产出：{int(die_count * yield_rate)} 颗晶片")

import numpy as np

class WaferDefectMonitor:
    def __init__(self, threshold=150):
        self.defect_history = []
        self.threshold = threshold  # 缺陷总数报警上限
        
    def add_scan_data(self, lot_id, defect_count):
        self.defect_history.append(defect_count)
        # 保持最近50批数据
        if len(self.defect_history) > 50:
            self.defect_history.pop(0)
            
        # 计算移动平均 (Moving Average) 消除偶发波动
        avg_defects = np.mean(self.defect_history[-10:]) if len(self.defect_history) >= 10 else 0
        
        status = "✅ 正常"
        if defect_count > self.threshold:
            status = "🚨 紧急停线！颗粒爆发！"
        elif defect_count > avg_defects * 1.5:
            status = "⚠️ 趋势上升，需排查机台过滤器"
            
        return {
            "lot_id": lot_id,
            "current": defect_count,
            "10批平均": round(avg_defects, 1),
            "状态": status
        }

# 模拟日常监控
monitor = WaferDefectMonitor(threshold=120)
# 某批次扫描发现突然增多
alert = monitor.add_scan_data("Lot_A2026", 145)
print(alert)