In the name of Allah, Most Compassionate, Most Merciful,
To begin with, the majority of the classical scholars are of the opinion that the post-sunrise prayer (ishraq) is the same as the mid-morning prayer (Duha). This is the very reason why the major classical books of Hanafi Fiqh do not mention the two prayers separately. (See: Abu Bakr al-Jassas, Ahkam al-Qur�an, 3/559)
However, the common perception (especially amongst the Hanafis of the Indian Subcontinent) is that Salat al-Ishraq and Salat al-Duha are two separate prayers. The recommended time for offering Ishraq prayer is immediately after sunrise, whilst the Duha prayer (which they call the Chasht prayer) is offered later on. (See: Heavenly Ornaments, P: 143)
The reasoning behind this, in my humble view, is that the Messenger of Allah (Allah bless him & give him peace) has encouraged offering this prayer directly after sunrise. Sayyiduna Anas ibn Malik (Allah be pleased with him) narrates that the Messenger of Allah (Allah bless him & give him peace) said: �Whosoever offers his morning (fajr) prayer in congregation, then remains seated making the dhikr of Allah until the sun rises, and thereafter offers two rakats, they will receive the reward of performing a Hajj and Umrah.� (Sunan Tirmidhi, no: 586)
This Hadith implies that one should offer this optional prayer directly after sunrise by remaining seated on the very place one offered the Fajr prayer and by engaging in d’ua and other forms of dhikr. Thereafter, when the sun has risen properly, one should offer the Ishraq or Duha prayer.