• Ideal Diode Equation

• Reverse Saturation Current Equation

• Ideality Factor Equation

• Piecewise Diode Equation

• Forward Recombination Current Equation

• High Level Ijection Applied Voltage Equation

• Reverse Biase Avalanche Current Breakdown Equation

描述二极管的不同方程，描述了二极管不同工作范围的特点。Ideal Diode方程描述了二极管两端电压在以下范围内的特性：

在上述公式中，Vbr是反向击穿电压；Eg是二极管的 带隙电压 ，在300k时，Eg大约为1.12V.

根据k=1.381e-23; q = 1.602e-19,T=300，那么 kT/q=25.85mV。5kT/q=0.1293V。

以下是整流二极管(1)N4002）的分段I-V关系。

从上述公式来看，当电压低于一定程度时，I-V的关系已经不在呈现模型所描述的情况了。因此，存在以下问题：

• 关系到底是什么？
• 用实验来测量这种关系，并进一步解释原因。

由图1可以看出，我们需要测量的电流范围应该在 1 0 ? 12 ? 1 0 ? 9 10^{ - 12} -10^{ - 9} 10?12?10?9之间，因此，需要能够测量在pA可以测量等级电路。以下使用 AA4531 fA级静电放大器 模块来进行测量。在面包板上搭建如下电路：

测量输出的电流与输入电流之间的关系如下图所示：

u1=[0.00,0.00,0.01,0.01,0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.02,0.03,0.03,0.03,0.03,0.03,0.04,0.04,0.04,0.04,0.04,0.05,0.05,0.05,0.05,0.05,0.06,0.06,0.06,0.06,0.06,0.07,0.07,0.07,0.07,0.07,0.08,0.08,0.08,0.08,0.08,0.09,0.09,0.09,0.09,0.09,0.10,0.10,0.10,0.10,0.10,0.11,0.11,0.11,0.11,0.11,0.12,0.12,0.12,0.12,0.12,0.13,0.13,0.13,0.13,0.13,0.14,0.14,0.14,0.14,0.14,0.15,0.15,0.15,0.15,0.16,0.16,0.16,0.16,0.16,0.17,0.17,0.17,0.17,0.17,0.18,0.18,0.18,0.18,0.18,0.19,0.19,0.19,0.19,0.19,0.20,0.20,0.20,0.20]
c1=[0.10,0.12,0.13,0.15,0.17,0.19,0.21,0.23,0.25,0.27,0.29,0.32,0.34,0.36,0.39,0.41,0.44,0.46,0.49,0.52,0.55,0.58,0.61,0.65,0.68,0.73,0.76,0.80,0.84,0.88,0.92,0.96,1.00,1.04,1.08,1.13,1.18,1.21,1.26,1.31,1.36,1.41,1.46,1.51,1.56,1.61,1.67,1.73,1.79,1.84,1.90,1.96,2.02,2.08,2.14,2.21,2.27,2.34,2.41,2.48,2.54,2.62,2.69,2.76,2.83,2.90,2.98,3.06,3.13,3.20,3.28,3.35,3.43,3.52,3.60,3.72,3.80,3.89,3.97,4.06,4.14,4.23,4.32,4.41,4.49,4.59,4.68,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75,4.75]

u1=[0.00,0.00,0.01,0.01,0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.02,0.03,0.03,0.03,0.03,0.03,0.04,0.04,0.04,0.04,0.04,0.05,0.05,0.05,0.05,0.05,0.06,0.06,0.06,0.06,0.06,0.07,0.07,0.07,0.07,0.07,0.08,0.08,0.08,0.08,0.08,0.09,0.09,0.09,0.09,0.09,0.10,0.10,0.10,0.10,0.10,0.11,0.11,0.11,0.11,0.11,0.12,0.12,0.12,0.12,0.12,0.13,0.13,0.13,0.13,0.13,0.14,0.14,0.14,0.14,0.14,0.15,0.15,0.15,0.15,0.16,0.16,0.16,0.16,0.16,0.17,0.17,0.17,0.17,0.17,0.18,0.18,0.18,0.18,0.18,0.19,0.19,0.19,0.19,0.19,0.20,0.20,0.20,0.20]
c1=[-0.07,-0.05,-0.04,-0.03,-0.01,0.00,0.01,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.10,0.11,0.12,0.12,0.13,0.14,0.15,0.16,0.16,0.17,0.18,0.19,0.19,0.20,0.20,0.21,0.21,0.22,0.22,0.23,0.23,0.24,0.24,0.25,0.25,0.26,0.26,0.26,0.27,0.27,0.27,0.28,0.28,0.28,0.29,0.29,0.29,0.30,0.30,0.30,0.31,0.31,0.31,0.31,0.31,0.32,0.32,0.32,0.32,0.33,0.33,0.33,0.33,0.34,0.34,0.34,0.34,0.34,0.35,0.35,0.35,0.35,0.36,0.36,0.36,0.36,0.36,0.37,0.37,0.37,0.37,0.37,0.37,0.38,0.38,0.38,0.38,0.38,0.38,0.39,0.39,0.39,0.39,0.39,0.39,0.40]

#!/usr/local/bin/python
# -*- coding: gbk -*-
#============================================================
# MEAS1.PY -- by Dr. ZhuoQing 2020-07-01
#
# Note:
#============================================================
from headm import *
from tsmodule.tsvisa        import *
from tsmodule.tsstm32       import *
dp1308open()
dm3068open()
printf(meterval())
setv = linspace(0, 0.2, 100)
dp1308p6v(0)
time.sleep(5)
u1dim = []
c1dim = []
for v in setv:
    dp1308p6v(v)
    time.sleep(2)
    u1 = dm3068vdc()
    meter = meterval()
    c1 = -meter[0]
    printff(u1, c1)
    u1dim.append(u1)
    c1dim.append(c1)
tspsave('diodeiv', u1=u1dim, c1=c1dim)
plt.plot(u1dim, c1dim)
plt.xlabel("Voltage(V)")
plt.ylabel("Current(uA)")
plt.grid(True)
plt.show()
printf('\a')
#------------------------------------------------------------
# END OF FILE : MEAS1.PY
#============================================================

使用 RIGOL DP1308可编程电源，独立控制P25V和N25V的输出，通过电阻网络将它们合并在一起，形式一个可以有负电压平稳过渡到正电压的电压源。

上面的电阻网络在面包板上进行搭建。测量电流的电路部分与前面相同。

下面是测量施加电压从-4.5V增加到0.2V过程中电流的变化和数据。